Question 8 - A-Level Maths

Show that \(\sum _ { r = n } ^ { 2 n } r ^ { 3 } = \frac { 3 } { 4 } n ^ { 2 } ( n + 1 ) ( 5 n + 1 )\).
Hence find \(\sum _ { r = n } ^ { 2 n } r \left( r ^ { 2 } - 2 \right)\), giving your answer in a fully factorised form.