You have a cube made of 10 x 10 x 10 smaller
You have a cube made of 10 x 10 x 10 smaller cubes, for a total of 1000 smaller cubes. If you take off 1 layer of cubes, how many remain?
The remaining cube will be 8 x 8 x 8. This will be 512. A layer is take from all sides of the cube, so it would reduce the dimensions be two, not one.