A number theory problem by Akshat Sharda

Let a=(n+3)3n1a=\dfrac{(n+3)^3}{n-1} where aa and nn are integers.

Let the integral values of nn satisfying the above equation be n1,n2,n3,,nmn_{1},n_{2},n_{3}, \ldots, n_{m}.

Find (p=1mnp)+m\left(\displaystyle \sum^{m}_{p=1}n_{p}\right)+m.

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