Show that
$$\sum _ { r = 1 } ^ { n } 2 r \left( 2 r ^ { 2 } - 3 r - 1 \right) = n ( n + p ) ( n + q ) ^ { 2 }$$
where \(p\) and \(q\) are integers to be found.
Hence find the value of
$$\sum _ { r = 11 } ^ { 20 } 2 r \left( 2 r ^ { 2 } - 3 r - 1 \right)$$
(2 marks)