Write a Proof by Mathematical Induction of the Statement $1^{2}+3^{2}+5^{2}+\ldots+(2 n-1)^{2}=\frac{n(2 n-1)(2 n+1)}{3}$

Essay

Write a proof by mathematical induction of the statement:
$1^{2}+3^{2}+5^{2}+\ldots+(2 n-1)^{2}=\frac{n(2 n-1)(2 n+1)}{3}$