There is no need to count the number of 1x1x1 cubes on the surface directly. $$ $$ We can see that the core of the 4x4x4 cube is a 2x2x2 cube, and these inner cubes do not have paint on them. Since the core of the cube is made up of 8 smaller cubes, and the full cube is made up of 64 smaller cubes, then $64-8=56$ 1x1x1 cubes are painted.