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Sum of the cubes of the roots of $$x^3 - 15x^2 + 71x - 105 = 0$$ is
$$x = 3$$ is a root since $$27 - 135 + 213 - 105 = 0$$, and $$x^3 - 15x^2 + 71x - 105 = (x - 3)(x - 5)(x - 7)$$. The sum of the cubes of the roots is $$27 + 125 + 343 = 495$$.
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