This is exercise 3.1.1 of Computer Organization and Design, Revised 4th Edition.
Your math is correct. Check it with Wolfram Alpha.
31748 + 05228 = 37168
The solutions guide for the book says the answer is 7620. (That's what I can make out through the blur over page 68 on scribd.)
Of the four numbers in the table for that exercise, there is no pair that sums to 76208 or 762010, whether you interpret the numbers in the table as octal or decimal. The solutions guide is either wrong, or using a very obscure interpretation of the question.
Here's the Mathematica code I used to verify:
inputs = {3174, 0522, 4165, 1654, 8^^3174, 8^^0522, 8^^4165, 8^^1654}
Table[{i + j, BaseForm[i + j, 8]}, {i, inputs}, {j, inputs}] // Flatten // Sort // TableForm