$$ \frac{x^3+216}{x-6} \cdot \frac{x^2-12x+36}{x^2-6x+36} = \frac{(x+6)(x^2-6x+36)}{x-6} \cdot \frac{(x-6)^2}{x^2-6x+36} = (x+6)(x-6) = x^2 - 36 $$
Ответ: $$x^2-36$$