How many Rubik's Cube combinations are there?

...Well, lets start off easier and ask how many ways you can put the stickers on. If you number the stickers of each color 1-9, so that all 54 stickers are unique, there are about 231 duovigintillion ways to put them on the cube. That's 231 followed by a whopping 69 zeros. Let's get more complicated and ask how many ways you can arrange the pieces on it (now without numbering them). There are 8 corner pieces that can each be turned in 3 ways while in one spot, 12 edge pieces that can each be turned in 2 ways, and there are the center pieces that never change position. With that, there are about 519 quintillion (519 followed by 18 zeros) ways you can arrange the pieces on the cube. In order to get the real answer for the number of combinations on a Rubik's Cube, you have to take into account the fact that you can't get to every arrangement just by twisting the cube. I don't quite understand the math for this part, but Numberphile has made a video about it, revealing that there are exactly 43,252,003,274,489,856,000 Rubik's Cube combinations, or about 43 quintillion.

Here's a few Rubik's Cube videos made by Numberphile:

http://www.youtube.com/watch?v=QV9k6dRQQe4&list=PLt5AfwLFPxWJNAdHv8TUCOmj7iKqyHZeg