Hi
The possibilities are
1.x congruent to 0(mod 3) , y congruent to 0(mod 3) (for n>=2)
2.x congruent to 1(mod 3) , y congruent to 2(mod 3)
Case 1
Favourable outcomes= nC2
Case 2
Favourable outcomes=n^2

Hence the probability= (nC2+n^2) / (3n)C2 for n>=2....for n=1 it is n^2 / (3n)C2 as the first case is not possible
Do note that i have considered 1^3 + 2^3 and 2^3 + 1^3 as the same (which has to be the case as we just need to select nos) and also x not equal to y...
Hope it is right...
Shyam