Induction Proof

Prove that $5^{3^n}+1$ is divisible by $3^{n+1}$ for all nonnegative integers $n.$

What I did (or tried to do) was to use induction. I proved it worked for the base case $0,$ but I'm stuck on how to prove it works for $n=k+1$ if we assume it works for $n=k.$ Help!

--------Thanks!