Write a Proof by Mathematical Induction of the Statement:
1³ $n^{3}=\frac{n^{2}(n+1)^{2}}{4}$

Write a proof by mathematical induction of the statement:
1³ + 2³ + 3³ + ... + $n^{3}=\frac{n^{2}(n+1)^{2}}{4}$