Chapter 10 - Radical Functions and Equations - 10.2 - Graphing Cube Root Functions - Exercises - Page 556: 39

No

No. Odd functions are symmetrical to the origin and only some of the cube root functions (including the parent function) are symmetrical to the origin. Examples: $f(x)=x^3+5x$ is odd. $g(x)=x^3+x^2+5x+1$ is not odd. So, not all cube root functions are odd functions. Your friend is not correct.