Find integers a, b and c such that:
987654321a + 123456789b + c = (a + b + c)³
Note that x^3 - x = (x-1)x(x+1). Now let x = (a+b+c)
and rewrite the equation as
(x-1)x(x+1) = 987654320*a + 123456788*b.
Gerhard "Ask Me About System Design" Paseman, 2010.01.12
Well, the numbers cannot be more then something like 10^5, so a simple program that cycles through all possible a and b and sees if there's a corresponding c might give you an answer pretty fast -- I dunno, from a minute to a day depending on your computer and programming language.
This also depends on whether you also implement some trivial checks, like try it modulo 2, 3 and 5 first.