8. (a) Prove by induction, that for \(n \in \mathbb { Z } ^ { + }\), $$\sum _ { r = 1 } ^ { n } r ( 2 r - 1 ) = \frac { 1 } { 6 } n ( n + 1 ) ( 4 n - 1 )$$ (b) Hence, show that $$\sum _ { r = n + 1 } ^ { 3 n } r ( 2 r - 1 ) = \frac { 1 } { 3 } n \left( a n ^ { 2 } + b n + c \right)$$ where \(a\), \(b\) and \(c\) are integers to be found.