Question 6 - A-Level Maths

Show that $$( k + 1 ) \left( 4 ( k + 1 ) ^ { 2 } - 1 \right) = 4 k ^ { 3 } + 12 k ^ { 2 } + 11 k + 3$$
Prove by induction that, for all integers $n \geqslant 1$, $$1 ^ { 2 } + 3 ^ { 2 } + 5 ^ { 2 } + \ldots + ( 2 n - 1 ) ^ { 2 } = \frac { 1 } { 3 } n \left( 4 n ^ { 2 } - 1 \right)$$