So I started doing this proof then realized I hasn't really used induction. I said that n^3 + 5n is equal to n^3 - n + 6n = n(n^2 - 1) + 6n = n(n-1)(n+1) + 6n = (n-1)(n)(n+1) + 6n

Now I know that 6n is divisible by 6 and the product of 3 consecutive integers is divisible by 6 so that the entire term is divisble by 6 but I don't know how to write a proper proof using that explanation. I know you can do this using induction although im not sure how. Thanks for your help