Determine whether or not there are any positive integral solutions of the simultaneous equations $$x_1^2+x_2^2+\cdots+x_{1985}^2=y^3\\\\ x_1^3+x_2^3+\cdots+x_{1985}^3=z^2$$ with distinct integers $x_1,x_2,\cdots,x_{1985}$.