Chapter 12.4, Problem 14SB

In Problems 1-22, use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers $n$.

$1^3\text{ + }{2}^3\text{ + }{3}^3\text{ + }\mathrm{...}\text{ + }{n}^3\text{ = }\frac{1}{4}{n}^2{\left(n\text{ + 1}\right)}^2$