Chapter E, Problem 39E

To determine

To prove: The formula (e) ${\displaystyle \sum _{i=1}^n{i}^3={\left[\frac{n\left(n+1\right)}{2}\right]}^2}$ of Theorem 3 using a method similar to that example 5, solution 1, start with ${\left(1+i\right)}^4-i^4$ .