How to compute the smallest integer which is sum of cubes in 13 ways? I would like to know the smallest integer which is sum of three positive cubes in 13 ways, such that $1^3+2^3+3^3=2^3+1^3+3^3$ are same ways of representation? What kind of theory there is behind that? I saw the question Sum of squares in at least 64 ways? but I don't know if that can be generalized as I'm not sure how to generalize Gaussian integers.

I guess it is 
119095488
= 24^3+204^3+480^3
= 48^3+ 85^3+491^3
= 72^3+384^3+396^3
= 113^3+264^3+463^3
= 114^3+360^3+414^3
= 149^3+336^3+427^3
= 176^3+204^3+472^3
= 190^3+279^3+449^3
= 207^3+297^3+438^3
= 226^3+332^3+414^3
= 243^3+358^3+389^3
= 246^3+328^3+410^3
= 281^3+322^3+399^3

The solution was given by Matti K. Sinisalo in http://keskustelu.suomi24.fi/node/12866739
