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

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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