8. (a) Use the standard results for \(\sum _ { r = 1 } ^ { n } r\) and \(\sum _ { r = 1 } ^ { n } r ^ { 2 }\) to show that $$\sum _ { r = 1 } ^ { n } \left( 3 r ^ { 2 } + 8 r + 3 \right) = \frac { 1 } { 2 } n ( 2 n + 5 ) ( n + 3 )$$ for all positive integers \(n\). Given that $$\sum _ { r = 1 } ^ { 12 } \left( 3 r ^ { 2 } + 8 r + 3 + k \left( 2 ^ { r - 1 } \right) \right) = 3520$$ (b) find the exact value of the constant \(k\).