Cubes of a cubic

Algebra Level 4

Let the roots of the cubic equation ${ x }^{ 3 }-3{ x }^{ 2 }+5x-7$ be $\alpha, \beta \quad and \gamma$ . Then find $\alpha ^{ 3 }+\beta ^{ 3 }+\gamma ^{ 3 }$

This problem is a part of my set The Best of Me