Fun with numbers

Let \((x_{1},y_{1}), (x_{2},y_{2}), (x_{3},y_{3}),\ldots, (x_{n},y_{n})\) be the ordered pairs of integers that satisfy the equation \(x^{3} + y^{3} = (x+y)^{2}\).

Express your answer as \(\displaystyle\sum_{i=1}^n (x_{i} + y_{i})\).

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