Answer
$44,000$
Work Step by Step
... we want to apply $(8)\displaystyle \qquad \sum_{k=1}^{n}k^{3}=\left[\frac{n(n+1)}{2}\right]^{2}$,
but the index does not start at 1.
$\displaystyle \sum_{k=5}^{20}k^{3}=$ (terms from 5 to 20) = (20 terms) - (first 4 terms)
$=\displaystyle \sum_{k=1}^{20}k^{3}-\sum_{k=1}^{4}k^{3}$
... use formula (8)
$=\displaystyle \left[\frac{20(20+1)}{2}\right]^{2}-\left[\frac{4(4+1)}{2}\right]^{2}$
$=210^{2}-10^{2}$
$=44,000$
