1. **Problem:** Calculate the contour integral $$\oint_C \frac{z}{(z-3)^3} \, dz$$ where $$C: |z|=1$$. 2. **Step 1: Identify singularities inside the contour.** The singularity is at $$z=3$$. Since $$|3|=3 > 1$$, the singularity is outside the contour $$|z|=1$$. 3. **Step 2: Apply Cauchy's theorem.** Since the function is analytic inside and on the contour (no singularities inside), the integral is zero: $$\oint_C f(z) \, dz = 0$$. **Final answer:** $$0$$.