Well, I have the following code:

Needs["Combinatorica`"];
x = 3051;
threetriples = 
  KSubsets[If[
    Length[Select[
       Select[PowersRepresentations[x, 3, 2], Times @@ # != 0 &], 
       Length[#] == Length[Union[#]] &]] >= 7, 
    Select[Select[PowersRepresentations[x, 3, 2], Times @@ # != 0 &], 
     Length[#] == Length[Union[#]] &], Nothing], 3];
testallperms[
   three_] := ({n1, n2, n3, n4, n5, n6, n7, n8, n9} = Flatten[three];
   Do[{n1, n2, n3, n4, n5, n6, n7, n8, n9} = 
     NextPermutation[{n1, n2, n3, n4, n5, n6, n7, n8, n9}];
    If[x == n1^2 + n2^2 + n3^2 == n4^2 + n5^2 + n6^2 == 
      n7^2 + n8^2 + n9^2 == n1^2 + n4^2 + n7^2 == 
      n2^2 + n5^2 + n8^2 == n3^2 + n6^2 + n9^2 == 
      n1^2 + n5^2 + n9^2, {n1, n2, n3, n4, n5, n6, n7, n8, n9}, 
     Nothing], {9!}]);
DeleteCases[Map[testallperms[#] &, threetriples], Null]

This came from a question I had yesterday.

Now, I have two questions about this:

1. The code takes round about 30 minutes to run, is there a way to speed up the calculation?
2. The code gave no solution which is not right, because when:

$$n_1=29,n_2=41,n_3=23,n_4=1,n_5=37,n_6=41,n_7=47,n_8=1,n_9=29$$

this must gave a solution to the code. So where is the mistake?