If the cube of $n$ is divisible by $3$, then $n$ is divisible by $3$ Trying to figure the statement $3|n$ iff $3|n^3$. While proving the forward direction was easy and stuck on the reverse direction. Any ideas?

By Euclid's lemma we have $3$ divides $n^3=n\times n^2$ so $3$ divides $n$ or divides $n^2$ and in this last case we apply this lemma again and we have the desired result.
