Calculate the sum of the coordinates of all pairs of positive integers (n, k) such that k \equiv 0, 3 \pmod{4}, n > k, and \sum\limits_{i=k+1}^{n} i^3 = (96^2 \cdot 3 - 1) \left(\sum\limits_{i=1}^{k} i\right)^2 + 48^2.
Calculate the sum of the coordinates of all pairs of positive integers (n, k) such that k \equiv 0, 3 \pmod{4}, n > k, and \sum\limits_{i=k+1}^{n} i^3 = (96^2 \cdot 3 - 1) \left(\sum\limits_{i=1}^{k} i\right)^2 + 48^2.