For what natural $n$ does $3^n > n^3$ hold true? Prove by induction 
For what natural $n$ does $3^n > n^3$ hold true? 

I figured that it holds true for all $n$ except $n = 3$. I am not sure how to prove it by induction. I proved it by $p(k) \implies p(k+1)$ but that doesn't show that $n \neq 3$ 

For $n=4$ we have
$$3^n> n^3$$ is true.
Let $$3^n> n^3$$ for all $n>3$.
Thus, $$3^{n+1}=3\cdot3^n>3n^3$$ and it's enough to prove that
$$3n^3>(n+1)^3$$ or
$$\sqrt[3]3n> n+1,$$ which is true for $n>3.$
