You are given a cube that is made with the help of 10x10x10 smaller cubes summing up to a total of 1000 smaller cubes. You are asked to take off one layer of the cubes.

How many remain now?

512

A layer will mean to remove from all sides of the cube. Thus it would reduce the dimension be two not one. In this way only a cube of 8x8x8 will remain. This totals to be 512.