**\(x\)** and **\(y\)** are the natural numbers satisfying following system of equations.

**\(y^{3}+3y = x^{3}+3x^{2}+ 266\)**

**\(x^{2}+y^{2} = 8x+8y+2\)**

Find the sum of the digits of the product of \(x\) and \(y\).

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