\[\large{\begin{align}\sum_{r=1}^{2016} r^3\binom{2016}{r} \end{align}} \]

If the value of the summation above is equal to \(A\), find the sum of digits of the number \( \dfrac A{2016\times 2^{2016}} \) when it is written in decimal representation.

(This problem is not original)

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