Answer: Option D
$$\eqalign{
& x - \frac{1}{x} = 2{\text{ to find }}{x^3} - \frac{1}{{{x^3}}} \cr
& \Rightarrow x - \frac{1}{x} = 2 \cr
& \left[ {{\text{Cubing both sides}}} \right] \cr
& \Rightarrow {\left( {x - \frac{1}{x}} \right)^3} = {\left( 2 \right)^3} \cr
& \Rightarrow {x^3} - \frac{1}{{{x^3}}} - 3 \times x \times \frac{1}{x}\left( {x - \frac{1}{x}} \right) = 8 \cr
& \Rightarrow {x^3} - \frac{1}{{{x^3}}} - 3 \times \left( 2 \right) = 8 \cr
& \Rightarrow {x^3} - \frac{1}{{{x^3}}} = 14 \cr} $$