Question

if you had a rubik's cube with 10 little squares on each side, and peeled off the outer layer, how many little cubes would you end up with?

Answer 1

solution:

The whole cube is made from 10³ = 1000 small cubes, but it would not be possible to make a practical mechanism for rotating the faces.  

Peeling off the outer layer of cubes leaves 8³ = 512 small cubes.