Sum of the given series will be

Calculus Level 3

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

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.