The cube $S$ with side $2$ consists of $8$ unit cubes.
Define block a figure that is formed from a cube $S$ as a result of the removal of one unit cube.
Decide if the cube with dimensions $2^n\cdot 2^n\cdot 2^n$ from which one cube has been removed can be built by blocks.
HINT
Since a block is formed by $7$ unit cubes we just need to prove that
$$7|2^{3n}-1=8^n-1$$
if you want to proceed by induction let consider
base case: $n=1$
induction step: assuming $7|8^n-1$ prove that $7|8^{n+1}-1$