Sum of the given series will be

Calculus

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

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.