sequences and series - Mathematical Induction: Sum of first n odd perfect cubes

The series is $$P_k: 1^3 + 3^3 + 5^3 + ... + (2k-1)^3 = k^2(2k^2-1)$$ and I have to replace
$P_k$ with $P_{k+1}$ to prove the series.

I have to show that $$k^2(2k^2-1) + (2k-1)^3 = (k+1)^2[2(k+1)^2-1]$$
I'm sorry that I'm asking but their are just so many factors the algebra just passes over my
head. Any help is appreciated.