\[\large \frac 7{2^3} + \frac {19}{6^3} + \frac {37}{12^3} + \frac {61}{20^3} + \cdots = \ ? \]

Note that

In the sequence \(7,19,37,61,\ldots\), the difference between each consecutive terms follows an arithmetic progression.

In the sequence \(2,6,12,20, \ldots\),the difference between each consecutive terms follows an arithmetic progression as well.

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