7. (a) Use the results for \(\sum _ { r = 1 } ^ { n } r\) and \(\sum _ { r = 1 } ^ { n } r ^ { 2 }\) to show that $$\sum _ { r = 1 } ^ { n } ( 2 r - 1 ) ^ { 2 } = \frac { 1 } { 3 } n ( 2 n + 1 ) ( 2 n - 1 )$$ for all positive integers \(n\).
(b) Hence show that $$\sum _ { r = n + 1 } ^ { 3 n } ( 2 r - 1 ) ^ { 2 } = \frac { 2 } { 3 } n \left( a n ^ { 2 } + b \right)$$ where \(a\) and \(b\) are integers to be found.