According to the formula,

The average of squares of first 'n' natural numbers =$\frac{(n+1)(2n+1)}{6}$

Here, n=25

∴ Required average 

$$\begin{gathered} =\frac{\left(25+1\right)\left(2\times 25+1\right)}{6} \\ =\frac{26\times 51}{6} \\ =\frac{1326}{6}= 221 \end{gathered}$$

Hence, Option C is correct.