Cube Hunting

Find all solutions to the equation 2n3+6n2+102n+98  =  m3m,nZ  . 2n^3 + 6n^2 + 102n + 98 \; = \; m^3 \hspace{2cm} m,n \in \mathbb{Z} \;. If the answers are (m1,n1),(m2,n2),,(mN,nN)(m_1,n_1)\,,\,(m_2,n_2)\,,\,\ldots\,,\,(m_N,n_N), evaluate S  =  j=1N(mj2+nj2)  . S \; = \; \sum_{j=1}^N (m_j^2 + n_j^2) \;.

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