CASE 1: the last digit of n is 0. in this case sum_of_digits_of (n+3)= 3 + sum_of_digits_of n. So the inductive statement holds.
CASE 2: the last digit of n is 1. same argument holds.
CASE 8: the last digit of n is 7. here the argument extends to the second last digit if the second last digit is less than 9 and to the third last digit if the third last digit is 9 and so on. But still the argument is easy. Can you finish?