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

Let the words numbers be be (x+2) and (x)
then we get equation

(x+2)^3 - x^3 - (2x^2 + 4x+ 4) = 400
(not solving further as this a sum of brilliant's this week challenge0