If $\mathrm{C}_0, \mathrm{C}_1, \mathrm{C}_2, \ldots, \mathrm{C}_8$ are the binomial coefficients in the expansion of $(1+x)^8$ then $\sum_{r=1}^8 r^3 \frac{\mathrm{C}_r}{\mathrm{C}_{r-1}}=$

• Correct answer
  A

  $540$
• B

  $336$
• C

  $105$
• D

  $270$

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