3. (a) Show that \(r ^ { 3 } - ( r - 1 ) ^ { 3 } \equiv 3 r ^ { 2 } - 3 r + 1\)
(b) Hence prove by the method of differences that, for \(n \in \mathbb { Z } ^ { + }\) $$\sum _ { r = 1 } ^ { n } r ^ { 2 } = \frac { n ( n + 1 ) ( 2 n + 1 ) } { 6 }$$ [You may use \(\sum _ { r = 1 } ^ { n } r = \frac { n ( n + 1 ) } { 2 }\) without proof.]