If $$x = 2 + \sqrt3$$, then the value of $$x^3 - x^{-3}$$ is:

Given, $$x=2+\sqrt{3}$$

$$=$$> $$\ \frac{1}{x}=\ \frac{1}{2+\sqrt{3}}$$

$$=$$> $$\ \frac{1}{x}=\ \frac{1}{2+\sqrt{3}}\times\ \frac{2-\sqrt{3}}{2-\sqrt{3}}$$

$$=$$> $$\ \frac{1}{x}=\ \frac{2-\sqrt{3}}{4-3}$$

$$=$$> $$\ \frac{1}{x}=\ 2-\sqrt{3}$$

$$\therefore\ x-\frac{1}{x}=(2+\sqrt{3})-(2-\sqrt{3})=2\sqrt{3}$$

$$=$$> $$\left(\ x-\frac{1}{x}\right)^3=\left(2\sqrt{3}\right)^3$$

$$=$$> $$x^3-\frac{\ 1}{x^3}-3.x.\frac{1}{x}\left(\ x-\frac{1}{x}\right)=8\left(3\sqrt{3}\right)$$

$$=$$> $$x^3-\frac{\ 1}{x^3}-3\left(2\sqrt{3}\right)=24\sqrt{3}$$

$$=$$> $$x^3-x^{-3}=30\sqrt{3}$$

Hence, the correct answer is Option C