One has to specify it completely
In[7]:= FindInstance[(10 x1 + x2)^3 + (10 x2 + x1)^3 == y^2 && y > 0 &&
0 < x1 < 10 && 0 < x2 < 10, {x1, x2, y}, Integers]
Out[7]= {{x1 -> 5, x2 -> 6, y -> 671}}
and yes
In[5]:= Sqrt[56^3 + 65^3]
Out[5]= 671
56 is a solution and 56 is
the solution:
In[8]:= FindInstance[(10 x1 + x2)^3 + (10 x2 + x1)^3 == y^2 && y > 0 &&
0 < x1 < 10 && 0 < x2 < 10, {x1, x2, y}, Integers, 4]
Out[8]= {{x1 -> 5, x2 -> 6, y -> 671}, {x1 -> 6, x2 -> 5, y -> 671}}
