radman:
There are 8 corner mini-cubes each of which have 3 colors, and there are 12 edge mini-cubes each of which have 2 colors - so that is where the numerator comes from. I am not sure about the denominator.
I expect the denominator has to do with symmetries, (not sure)
- The 12 edge minicubes are swapped by two.
- The 8 corners are swapped by three and that can be done in two ways