Dr. Pepper-
The Rubik’s cube puzzle will take time and smarts, neither of which I have right now.
Here are the facts I think need to be factored into getting the answer:
1) Corner pieces. There are eight corner pieces, each of which can be on any corner, independent of the other seven corner pieces. Each piece can have three different positions on each corner.
2) Center pieces. There are six center pieces. They are not completely independent of each other, since two opposing colors will always oppose each other.
3) Side pieces. There are twelve side pieces, each of which can be on any side, independent of the other eleven side pieces. Each piece can have two different positions on each side.
What has to be calculated is corner-piece-combos * center-piece-combos * side-piece-combos.
Calculating by colored squares won’t work since all colors are locked immovably to one or two other colors, except for the center pieces.