Cubes Within Cubes


$3\times 3\times3$ covers a single cube and a $5\times 5\times$ covers that.

The cubes you need are:

$5^3=125$, $6^3=216$, $7^3=343$, $8^3=512$, $9^3=729$, $11^3=1331$, $13^3=2197$, $15^3=3375$.