Infinite sum question

Calculus Level 4

\[ \large \dfrac{1^3}{3^1} + \dfrac{2^3}{3^2} + \dfrac{3^3}{3^3} + \dfrac{4^3}{3^4} + \cdots \]

If the series above is equal to \( \dfrac pq\), where \(p\) and \(q\) are coprime positive integers, find \(p+q\).

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