You have a 3x3x3 rubik's cube. You'd like to split it into 27 single cubes (1x1x1), with "cuts". Before each cut, you can place the pieces of the cube anyway you'd like, and you can pass one plane (one "cut of a knife", if you'd like).
It can be done rather trivially with six cuts (see below). Can you do it in less than six? If yes, show, otherwise prove it can't be done.
