1. **State the problem:** Evaluate the expression $1-\frac{1}{27}x^3$ when $x=-3$. 2. **Recall the formula:** The expression is $1-\frac{1}{27}x^3$. 3. **Substitute the value:** Replace $x$ with $-3$: $$1-\frac{1}{27}(-3)^3$$ 4. **Calculate the cube:** $(-3)^3 = -27$. 5. **Simplify the fraction:** $$1 - \frac{1}{27} \times (-27) = 1 - (-1)$$ 6. **Simplify the expression:** $$1 + 1 = 2$$ **Final answer:** $2$