Quick question on Proof and divisibility

[Glavinsolo]

I have a question on how to prove the following

Prove that "n(n^2+8) is divisible by 3" for all positive integers n.

I proved the basis by plugging in 1 and doing the answer mod 3 to get 0.

now I am at the part where I came to and stopped

((n+1)((n+1)^2 + 8)) = ?

If you have any knowledge as to what would push me to completing this to show that it is divisible by 3.

 

[Maximus Power]

If thats not OT, I don't know what is.

 

[Glavinsolo]

How about this can anyone tell me how

2^k + 4 < 2^k + 2^k = 2×2^k = 2^1×2^k = 2^k+1

Then 4(k+1) < 2^k+1, and (*) holds for n = k + 1.