proof verification - Prove or Disprove Inequality By Induction

Prove or Disprove

$\sum_{i=0}^n(2i)^3 \le (8n)^3$

If true, prove using induction. If false, give the smallest value of n that is a counter example and the values for the left and right hand sides of the equation.

I started out with the Base Case at n = 1:

$\sum_{i=0}^1(2i)^3 = 8, 8^3 = 512$

$8 \le 512 \therefore$ true

Induction Hypothesis: Assume
$\sum_{i=0}^k(2i)^3 \le (8n)^3$ is true

Induction: $\sum_{i=0}^{k+1} (2i)^3 \le (8(k+1))^3$

$\sum_{i=0}^{k+1} (2i)^3 = \sum_{i=0}^k(2i)^3 + (2(k+1))^3$

This is where I'm stuck in the problem right now. I'm not sure how to use the hypothesis when it's an inequality.