Find the sum of the series up to \(n\) terms

\(1^2 + (2 \times 2^2) + 3^2+ (2 \times 4^2)+\cdots +n^2\).

Where \(n\) is an odd number.

i.e Evaluate

\(\large \displaystyle {\sum_{m = 1}^ {n} \left ( (2m-1)^2+[2 \times(2m)^2] \right ) } \)

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