Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.1 Sequences - 12.1 Assess Your Understanding - Page 808: 79

$44000$

I know that $\sum_{k=1}^{n} (k^3)=\left[\frac{n(n+1)}{2}\right]^2.$ Hence $\sum_{k=5}^{20} (k^3)=\sum_{k=1}^{20} (k^3)-\sum_{k=1}^{4} (k^3)=\left[\frac{20(20+1)}{2}\right]^2-\left[\frac{4(4+1)}{2}\right]^2=44100-100=44000$