First, it's spelled Rubik, not Rubic.  Erno RubiK is a Hungarian mathematician who figured out how to make the cube sometime in the mid-seventies. He applied for a patent on it in Hungary in 1975, and he had come up with the idea in 1974. The first prototype was build in 1977, and the first commercial procution units in 1977. The first sales were in 1978, in Hungary. Sometime late that year or in early 1979 a copy of the cube made it to the UK and into the hands of David Singmaster, a university mathematician, who published a small tract on it that circulated inside the community of professional academic mathematicians, who understood it immediately to be a cunning example of what is called a permutation group in algebra. 

Ideal Toy signed a deal to make the cubes for distribution as a puzzle or toy in September of 1979, and they made there international debut at several toy fairs in London, Paris, Nuremberg, and New York in 1980. The Ideal Toy version of the cubes used a slightly different and improved internal mechanism from the original Hungarian version to conform to safety and packaging standards in the US, and these changes made it smoother and easier to work as well.  The original Ideal Toy version at the first toy fair was called The Gordian Knot, until someone suggested Rubik's Cube.  In other countries and under other licenses it is also called the Hungarian Cube, the Magic Cube, The Cube, and Rubik Cube.  A smaller version of it that is 2 X 2 x 2 (called Rubik's Mini Cube), and also larger versions of it that are 4 X 4 X 4 (Rubik's Revenge) and 5 X 5 X 5 (Rubik's Professor Cube) have been produced commercially and are still available for sale, but I know of no larger cube that has been produced. There are, however, many other variants on the cube which have slightly different shapes, ranging from a pyramid to some odd shapes that are worked by similar means.  There are even versions which have pieces that are different sizes and shapes, i.e., not all the component pieces are the same. There are at least sixty different physical versions that derive from it, and I own a copy of most of them.

An interesting sidelight.  The first versions of the cube that were produced by Ideal Toy had Blue and White opposite each other, Red and Orange, and Green and Yellow. But there were always other configurations (either those manufactured under other licenses or knock-off copies), and some of these used different colors (a common one used black on one side) or different orientations, the most common being Yellow opposite White, Red opposite Orange, and Blue opposite Green, and it's this last version which has now become standard for the licensed manufactured cube world-wide.

Following its debut in the US in 1980, the cube became a craze, with Ideal shipping over 100 million cubes in three years.

There are several ways to solve the cube, all pretty difficult to work out, but the one that was published was by a junior high school boy named Patrick Bossert, who was twelve at the time.  His small pamphlet sold over 1.5 million copies.

One of the most interesting discoveries about the cube, made by a high school math teacher in Virginia, was that the number of configurations on the cube is exactly one more than a prime number; in other words, if you exclude the one single restored configuration, the number of remaining, unrestored, configurations is a prime.  Amazing.

I saw my first cube in late 1979 and, along with Evar Nering, solved it in six hours one evening and later improved the solution, which we wrote a book about. Unlike some of the other solution manuals, ours gave a very nifty solution, but also the mathematics behind it. Our book, which came out in 1980, was called The Cubemaster's Sourcebook.  Others who were active in writing about the cube were David Singmaster and Morwen Thistlewhwaite in the UK, Razid Black in the US and others. Nering and I proved that there is at least one configuration that requires 19 moves to reach, and we proved you can always solve it in 52 moves (although these moves require a special catalog). Morwen Thistlethwaite also proved that the cube can always be solved in 52 moves, although we use slightly different definitions of a move.  Since 1980 the minimum number of moves to solve it has been lowered, using computers, to 50.  No one knows for sure what the actual minimum is, but most of us who have worked on it believe that it is close to the 19 which Nering and I discovered is required by at least one configuration. Most betting is on a final solution, the so-called God's Algorithm for the cube, in the low twenties.

The algorithm we published for the solution optimizes speed of restoration and ease of manipulation based on simple visual cues, and is guaranteed to produce a solution in no more than 65 (very fast and easy) moves. We were able to restore the cube from a random position in about 45 seconds, and some of our students, who were faster physically than we were, could do it in about 30 to 35.

Nering and I also solved, using an extension of our algorithm, called the Freewheeling Algorithm, all other versions of the cube, including the 4 X 4 X 4, 5 X 5 X 5, 6 X 6 X 6, and 7 X 7 X 7, and we proved that the moves in the Freewheeling Algorithm for the 7 X 7 X 7 version were sufficient to do any size cube (N X N X N) even if the cube is impossible to manufacture physically.

The cube is unbelieveably hard to solve.  The number of possible combinations on even the 3 X 3 X 3 is about 43 sextillion, and there is only one solution (if you take into account the orientations of the centers, which you have to do if, for instance, there is a pattern or logo on each face).  That's what made it a fad, and a frustration for so many; even good puzzle solvers, who were used to takling hard puzzles, usually couldn't get it without reading a solution book.

To calculate the number of possible configurations on the cube, note that corners always go to corners, edges to edges, and the centers remain centers.  So we just have to calculate how many of these moves are possible. With the 8 corners, there are 8! = 40,320 possible rearrangements (if they're all possible; more about that in a minute), and each corner has 3 different possible orientations, so there can be 3 to the 8th possible orientations of the corners.

However, with the way the cube works, not all of these orientations are possible.  It's only mildly difficult to prove that once the first 7 corners are oriented, the orientation of the 8th is determined uniquely, so there are only 3 raised to the 7th power, or 2,187, orientations possible. Therefore, the number of possible arrangements of the corners, is 40,320 X 2,187 = 88,179,840.  By the same kind of analysis, we can see that there are, among the 12 edge pieces, 12! = 479,001,600 ways to locate the edges, but on the actual cube once 11 of these are set the location of the 12^th one is fixed (you can't swap only two edges), a fact that can be proved by noting that a certain kind of parity among the edges is preserved by every rotation, so there are half this many ways of arranging the edge pieces, or 239,500,800 in total.  But each edge can be in either of two orientations in its position, so you have to multiply this number by 2 to the 12th power.  Again, however, a subtle parity preservation on the actual cube means that once the orientations of 11 of the edges is set the orientation of the 12th is forced, so the number of orientations is 2 raised to the 11th power, or 2,048.  So the number of possible edge configurations is 239,500,800 X 2,048 = 490,497,638,400.If we consider only these configurations, which is all you have to consider on a standard cube, the number of possible configurations is the product of these two numbers, 88,179,840 x 490,497,638,400 = 43,252,003,274,489,856,000, or about 43 X 10 to the 18th, or 43 billion billion, which is also called 43 sextillion.

This is because the edges and corners are entirely independent of one another and nothing about the configuration of one affects the other. However, the centers of the cubes also move--they rotate, even though they stay in place.  Each of the 6 centers can be in any of 4 orientations, although a parity argument again can show that only half of these are possible since once the positions of 5 of the 6 centers is determined, the orientation of the 6th can take on only 2 of the possible 4 positions.  So the number of possible center orientations is 4 raised to the 6th power, divided by 2, or 2,048.  So to get the total number of possible configurations you have to multiply 43,252,003,274,489,856,000 by 2.048, to get the final total, 88,580,102,706,155,200,000,000, or about 89 times 10 to the 21st, or 89 septillion.

This is a big number.  Here's how big:  If you could search through 1 million of these possible configurations every second, it would take 2,807,164,641years to see them all; in other words, on average it would take half that, or 1,403,582,321years, about 1.4 billion, to stumble onto the solution.  With the larger versions of the cube this number gets ridiculously out of hand. With the 8 X 8 X 8 cube, the number of possible configurations is larger than the number of subatomic particles in the universe.