Headache while Summing!

we can observe a pattern,

$9^{2} = 81 Sum of digits = 9$

$99^{2} = 9801 Sum of digits = 18$

$999^{2} = 998001 Sum of digits = 27$

So,Sum of digits = $9 \times x$

Where,

$x = No. of digits$

Hence,

$\boxed{108}$

$999999999$

$= (1000000000 - 1)^2$

$= (10^{12} - 1)^2$

$=10^{24} - 2*10^{12} + 1$

$=999999999998000000000001$

So the sum of the digits is $11*9+8+1 = 108$