First, note that the larger cube is made up of 1000 smaller cubes.  The easiest way to think about this is how many cubes are NOT painted?  8 x 8 x 8 inner cubes are not painted which equals 512 cubes.  Therefore, 1000 – 512 = 488 cubes that have some paint.  Alternatively, we can calculate this by saying that two 10 x 10 sides are painted (200) plus two 10 x 8 sides (160) plus two 8 x 8 sides (128).  200 + 160 + 128 = 488.