According to the formula,

The average of the cubes of first 'n' natural numbers= $\frac{\mathrm{n}{\left(\mathrm{n}+1\right)}^2}{4}$

where, n=9

∴ Required average =$\frac{9x{\left(9+1\right)}^2}{4}=\frac{9\times 100}{4}$

= 9×25=225

Hence, Option D is correct.