1. **State the problem:** Find the limit $$\lim_{n \to 1} (n^3 - 6n + 1).$$ 2. **Recall the limit rule:** For polynomial functions, the limit as $n$ approaches a value is simply the function evaluated at that value. 3. **Evaluate the function at $n=1$:** $$1^3 - 6 \times 1 + 1 = 1 - 6 + 1 = -4.$$ 4. **Conclusion:** The limit is $$\boxed{-4}.$$