For $\displaystyle n \in \mathbb{Z}^+$, prove that $\displaystyle 2^{3n+2} + 5^{n+1}$ is divisible by $\displaystyle 3$. (Proof by induction)

Also, I am confused whether $\displaystyle (2^5-2^2).2^{3n} = 2^{3n+2}(2^3-1)$ is correct or not. Please help! I am STUCK on induction, and my exams are in two weeks.

Any other advice on solving induction questions would be great.

Cheers!