Proof by induction help. I seem to be stuck and my algebra is a little rusty

Stuck on a homework question with mathematical induction, I just need some help factoring and am getting stuck.

$\displaystyle \sum_{1 \le j \le n} j^3 = \left[\frac{k(k+1)}{2}\right]^2$

The induction part is: $\displaystyle \left[\frac{k(k+1)}{2}\right]^2 +(k+1)^3$ is where I am having a problem.

If you could give me some hints as to where to go since I keep getting stuck or writing the wrong equation.

I'll get to $\displaystyle \left[{k^2+2k\over2}\right]^2 + 2{(k+1)^3\over2}$

Any push in the right direction will be appreciated.

Answer

$(\frac{k(k+1)}{2})^2+(k+1)^3$

$=\frac{k^2(k+1)^2}{4}+(k+1)(k+1)^2$

$=\frac{(k+1)^2}{4}(k^2+4k+4)$

$=\frac{(k+1)^2}{4}(k+2)^2$