They're Not All The Same Degree!

x3+y33+xy=2007\large \dfrac {x^3+y^3}{3}+xy = 2007

Let there be nn unordered positive integral solutions to the above equation. Call these solutions (x1,y1),(x2,y2),,(xn,yn)(x_1, y_1), (x_2, y_2) , \ldots, (x_n, y_n). Find the value of

i=1nxiyi.\displaystyle \sum_{i=1}^n x_i y_i.

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