Chapter 4 - Section 4.6 - Cryptography - Supplementary Exercises - Page 307: 6

The statement given is true.

The square of an odd integer must be $1$ mod 4, so the sum of 2 squares of odd integers is $2$ mod 4. However, this is not a quadratic residue, so there can't exist a perfect square that is the sum of squares of odd integers, so the statement is true.