Prove or disprove: If $n^3$ is odd then $n$ is odd. If $n^3$ is odd, then $n$ is odd. 

I need to prove or disprove by means of counterexample why this is true or false.

$\forall x P(x) = x^3$, $x = 1,3,5,7,9$

I am having a very difficult time finding a way to prove this by counterexample!
Suppose $n^3$ is odd, but $n$ is not odd. Then $n$ must be even. The product of any two even numbers is even, so $n^2$ is even. Then $n(n^2)=n^3$ is the product of two even numbers again: and so $n(n^2)=n^3$ is even. This contradicts the assumption that $n^3$ is odd, and so $n$ is not even. So $n$ must be odd.
if $n$ is even, $n^3$ is even.
if $n$ is odd, $n^3$ is odd.


Therefore $n$ is odd iff $n^3$ is odd.