Let $[x]$ denote the greatest integer less than or equal to $x$. Then $\lim _{x \rightarrow 2^{+}}\left(\frac{[x]^3}{3}-\left[\frac{x}{3}\right]^3\right)=$

• A

  $0$
• Correct answer
  B

  $\frac{8}{3}$
• C

  $\frac{64}{27}$
• D

  $\frac{1}{3}$

Hence, the correct answer is option: 'B'.