3 variables, 2 equations, 1 answer

x+y=z2x2+y2=z3\large x + y = z^2\\ \large x^2 + y^2 = z^3

If positive integral solutions (x1,y1,z1),(x2,y2,z2),,(xn,yn,zn)(x_1, y_1, z_1), (x_2, y_2, z_2), \ldots, (x_n, y_n, z_n) satisfy the system of equations above, find the value of

i=1n(xi+yi+zi)\large \displaystyle \sum_{i=1}^n (x_i + y_i + z_i)

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