2. Given that for all real values of \(r , \quad ( 2 r + 1 ) ^ { 3 } - ( 2 r - 1 ) ^ { 3 } = A r ^ { 2 } + B\), where \(A\) and \(B\) are constants,
- find the value of \(A\) and the value of \(B\).
- Hence, or otherwise, prove that \(\sum _ { r = 1 } ^ { n } r ^ { 2 } = \frac { 1 } { 6 } n ( n + 1 ) ( 2 n + 1 )\).
- Calculate \(\sum _ { r = 1 } ^ { 40 } ( 3 r - 1 ) ^ { 2 }\).
(3)(Total 10 marks)