A wooden block shaped like a cube is painted on its four upright side faces only — the top and the bottom are left bare. It is then cut into 64 identical small cubes, 4 along each edge. How many of the small cubes carry no paint at all?

Look at any one horizontal layer from above: it is a 4 by 4 square of 16 small cubes, of which the 12 round the outside touch a painted side face and the 4 in the middle do not. Because the top and the bottom are bare, no layer loses its middle four, so all four layers contribute equally: $4\times 4=16$ clean cubes. The trap is 8: that is the answer for a cube painted on all six faces, where the top and bottom layers are stripped away as well, leaving only a $2\times 2\times 2$ core.