Given that $\sum_{r=1}^{n} r^2 = \frac{1}{6}n(n+1)(2n+1)$, find an expression, in simplified

Question

Given that $\sum_{r=1}^{n} r^2 = \frac{1}{6}n(n+1)(2n+1)$, find an expression, in simplified form, for $\sum_{r=n+1}^{2n} (2r-1)^2.$[6]

Accepted Answer

$\dfrac13n(28n^2-1)$

N1987 P1 Q19b