Correct Answer: $\frac{13}{8}$

Solution : Given: $2x-\frac{2}{x}=1$
Dividing both sides by 2, we get,
⇒ $x-\frac{1}{x} = \frac{1}{2}$
Cubing both sides, we get,
⇒ $(x-\frac{1}{x})^3=(\frac{1}{2})^3$
⇒ $x^3-\frac{1}{x^3}-3×x×\frac{1}{x}(x-\frac{1}{x})=\frac{1}{8}$
⇒ $x^3-\frac{1}{x^3}-3×\frac{1}{2}=\frac{1}{8}$
⇒ $x^3-\frac{1}{x^3}=\frac{1}{8}+\frac{3}{2}$
$\therefore x^3-\frac{1}{x^3}=\frac{13}{8}$
Hence, the correct answer is $\frac{13}{8}$.