Again thanks to the inputs I received from the answers above I tried with:

and again Wolfram|Alpha was unable to identify a saddle point.

I could have thought about it before, my fault, sorry for wasting your time.

Thanks to the responses received I tried with:

where also in this case the Hessian is null, but the saddle point is identified.

I conclude that the previous message "no saddle points found" is proper to interpret that the Wolfram | Alpha algorithms have not been able to identify any saddle points, but this does not imply that there cannot be.

Thank you all!

In Mathematica:

f[x_, y_, z_] := x^2 - y^2 + z^3;
SaddlePoint = Solve[{D[f[x, y, z], x] == 0, D[f[x, y, z], y] == 0, D[f[x, y, z], z] == 0}, {x, y, z}]
(*{{x -> 0, y -> 0, z -> 0}, {x -> 0, y -> 0, z -> 0}}*)

Det[( {
    {D[f[x, y, z], {x, 2}], D[D[f[x, y, z], x], y], 
     D[D[f[x, y, z], x], z]},
    {D[D[f[x, y, z], y], x], D[f[x, y, z], {y, 2}], 
     D[D[f[x, y, z], y], z]},
    {D[D[f[x, y, z], z], x], D[D[f[x, y, z], z], y], 
     D[f[x, y, z], {z, 2}]}
   } )] /. SaddlePoint[[1]]
  (*0*)

   (* Determinant gives a zero,(the test gives no information)  then we do not learn whether we have a local max, a local min, or a saddle point at (0,0,0)*)

Looks like WolframAlfa are correct.