Fewest saw cuts to dice a 4x4x4 block

A solid $4\times4\times4$ block of wood is to be sawn into $64$ unit cubes. Pieces may be rearranged and stacked between cuts, and each cut is one straight plane. What is the minimum number of cuts?

6. Halving each dimension twice, stacking the pieces before each cut, uses $2$ cuts per axis, so $6$ cuts suffice. Fewer is impossible: the unit cube in the interior of the block has six faces that are all fresh surfaces, and one planar cut can create at most one face of it.