1. **State the problem:** Simplify the expression $$\frac{x^3 - 27}{x - 3}$$. 2. **Recall the formula:** The numerator is a difference of cubes, which can be factored using the formula $$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$. 3. **Apply the formula:** Here, $$a = x$$ and $$b = 3$$, so $$x^3 - 27 = (x - 3)(x^2 + 3x + 9)$$. 4. **Substitute back into the expression:** $$\frac{x^3 - 27}{x - 3} = \frac{(x - 3)(x^2 + 3x + 9)}{x - 3}$$. 5. **Simplify by canceling common factors:** Since $$x \neq 3$$ (to avoid division by zero), cancel $$x - 3$$: $$= x^2 + 3x + 9$$. **Final answer:** $$x^2 + 3x + 9$$.