1. **State the problem:** We need to find the limit of the function $f(x) = x^3 - 1$ as $x$ approaches 1. 2. **Substitute the value:** Since $f(x)$ is a polynomial, it is continuous everywhere, so we can directly substitute $x = 1$ into the function. 3. **Calculate the value:** $$ \lim_{x \to 1} (x^3 - 1) = 1^3 - 1 = 1 - 1 = 0 $$ 4. **Conclusion:** The limit of $x^3 - 1$ as $x$ approaches 1 is 0.