(184, 345) find other couple of numbers such that

184 + 345 = 23^2

184^2 + 345^2 = 391^2

184^3 + 345^3 = 6877^2

Could you find other primitive pair of non-zero integers with the same property?

The aim is to find (x, y) such that

x + y = A^2

x^2 + y^2 = B^2

x^3 + y^3 = C^2

N.B. a primitive solution is a solution which is not a multiple of any smaller solution.