4. (a) Use the standard results for \(\sum _ { r = 1 } ^ { n } r ^ { 3 }\) and \(\sum _ { r = 1 } ^ { n } r\) to show that $$\sum _ { r = 1 } ^ { n } \left( r ^ { 3 } + 6 r - 3 \right) = \frac { 1 } { 4 } n ^ { 2 } \left( n ^ { 2 } + 2 n + 13 \right)$$ for all positive integers \(n\).
(b) Hence find the exact value of $$\sum _ { r = 16 } ^ { 30 } \left( r ^ { 3 } + 6 r - 3 \right)$$