According to the formula,

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

where n=5

∴ Required average

$$\begin{gathered} =\frac{5{\left(5+1\right)}^2}{4} \\ =\frac{5\times 36}{4} \end{gathered}$$ 

= 5×9=45

Hence, Option C is correct.