1. **State the problem:** Find the domain of the function $f(x) = x^3$. 2. **Recall the definition of domain:** The domain of a function is the set of all possible input values ($x$) for which the function is defined. 3. **Analyze the function:** The function $f(x) = x^3$ is a polynomial function. 4. **Important rule for polynomials:** Polynomial functions are defined for all real numbers because you can cube any real number without restriction. 5. **Conclusion:** Therefore, the domain of $f(x) = x^3$ is all real numbers. **Final answer:** $$\text{Domain} = (-\infty, \infty)$$