Proof by Induction $3^n > n^3$ I am trying to prove the following, however I'm stuck at the Induction hypothesis

Prove by induction that, for all integers $n$, if $n\geq 5$, then $3^n>n^3$

What I have Done:
Base Case:
$n = 5$
$3^5 > 5^3$
$243 > 125$ so TRUE
Assume True for $n = k$
$3^k > k^3$ must be TRUE
Should be TRUE for $n = k+1$
$3^k + 3^{k+1} > k^3 + 3^{k+1}$
Im a little stuck here. Any help would be appreciated!

Supposing that $3^k\gt k^3$, you need to prove $3^{k+1}\gt (k+1)^3$.
For inductive step : $$\begin{align}3^{k+1}&\gt 3k^3\\&=k^3+k^3+k^3\\&\gt k^3+3k^2+3^2k\\&=k^3+3k^2+3k+6k\\&\gt k^3+3k^2+3k+1\\&=(k+1)^3.\end{align}$$
