1. **State the problem:** Solve the equation $n \times n \times n = n + n + n$. 2. **Rewrite the equation:** The left side is $n^3$ and the right side is $3n$, so the equation becomes: $$n^3 = 3n$$ 3. **Bring all terms to one side:** $$n^3 - 3n = 0$$ 4. **Factor the equation:** $$n(n^2 - 3) = 0$$ 5. **Set each factor equal to zero:** - $n = 0$ - $n^2 - 3 = 0$ 6. **Solve for $n$:** - From $n = 0$, we get $n = 0$ - From $n^2 - 3 = 0$, we get $n^2 = 3$, so $n = \pm \sqrt{3}$ 7. **Final answer:** $$n = 0, \sqrt{3}, -\sqrt{3}$$ These are the values of $n$ that satisfy the original equation.