6. (a) Use the standard results for \(\sum _ { r = 1 } ^ { n } r ^ { 2 }\) and for \(\sum _ { r = 1 } ^ { n } r ^ { 3 }\) to show that, for all positive integers \(n\), $$\sum _ { r = 1 } ^ { n } r ^ { 2 } ( r + 1 ) = \frac { n } { a } ( n + 1 ) ( n + 2 ) ( 3 n + b )$$ where \(a\) and \(b\) are integers to be found.
(b) Hence find the value of $$\sum _ { r = 25 } ^ { 49 } \left( r ^ { 2 } ( r + 1 ) + 2 \right)$$