Question

If $1^3+2^3+3^3+......+n^3={\left(\frac{n(n+1)}{2}\right)}^2$. Find $1^3+2^3+3^3+......+{21}^3$

Answer 1

n=21

Substituting $n=21$ in$(\frac{n(n+1)}{2}{)}^2$

$Sum=(\frac{n(n+1)}{2}{)}^2$

$Sum=(\frac{21\times 22}{2}{)}^2$

$Sum=(21\times 11{)}^2=53361$

Hence the answer is $53361$