discrete mathematics - Use mathematical induction to prove that a function is divisible by 9

I initially posted a question and thought that was the only one I was stuck on, but there's this other question too.

I think I kinda solved it, but I'm getting that it isn't divisible by 9. I'd like a confirmation please!

The question is as follows:

Use mathematical induction to prove that

$$5^{2n+1} - 21n + 31$$ is divisible by $9$ for $\forall n \geq 1$.