If you want to cut a 3x3x3 cube in 1x1x1 pieces by using plane cuts, you would need six cuts, if no rearranging of pieces is allowed.
How many cuts would you need, if you were allowed to rearrange the pieces after each cut, and why?
For a 4x4x4 cube, the number of cuts is still 6, if we are allowed to rearrange pieces.