The difference of the cubes of two consecutive odd positive integers is 400 more than the sum of their squares. Find the sum of the two integers.

Answer 1

a^3 - b^3 = 400+a^2+b^2
also, a=b+2, so
(b+2)^3 - b^3 = (b+2)^2 + b^2 + 400
b=9, so a=11

11^3-9^3 = 1331-729 = 602
11^2+9^2+400 = 602