10. (i) Use the standard results for \(\sum _ { r = 1 } ^ { n } r ^ { 3 }\) and \(\sum _ { r = 1 } ^ { n } r\) to evaluate $$\sum _ { r = 1 } ^ { 24 } \left( r ^ { 3 } - 4 r \right)$$ (ii) Use the standard results for \(\sum _ { r = 1 } ^ { n } r ^ { 2 }\) and \(\sum _ { r = 1 } ^ { n } r\) to show that $$\sum _ { r = 0 } ^ { n } \left( r ^ { 2 } - 2 r + 2 n + 1 \right) = \frac { 1 } { 6 } ( n + 1 ) ( n + a ) ( b n + c )$$ for all integers \(n \geqslant 0\), where \(a , b\) and \(c\) are constant integers to be found.