- (a) Using the formula for \(\sum _ { r = 1 } ^ { n } r ^ { 2 }\) write down, in terms of \(n\) only, an expression for
$$\sum _ { r = 1 } ^ { 3 n } r ^ { 2 }$$
(b) Show that, for all integers \(n\), where \(n > 0\)
$$\sum _ { r = 2 n + 1 } ^ { 3 n } r ^ { 2 } = \frac { n } { 6 } \left( a n ^ { 2 } + b n + c \right)$$
where the values of the constants \(a\), \(b\) and \(c\) are to be found.