“The method (ALT+S in Face Select Mode) is not gives what I need, unless I did it the wrong way!!”
You need to be in Face Select Mode (I say this again, because your screenshot is in Vertex Select Mode) and Select (only) the outer Faces and then use ALT+S (together, not first ALT and then S). You also should not have ‘Emulate 3 Button Mouse’ enabled, because that messes up your ALT Shortcuts. Further more, make sure your Normals are consistent (SHIFT+N, with everything Selected) and you don’t have ‘double Vertices’ (M > Merge > By Distance, with everything Selected).
Those are the things I can think of now, that could mess things up.
And yes, it was perfectly clear what you were trying to do 😉
The Boolean Cube method works fine as well (with great control and flexibility), but is more work to set up, then the ALT+S method.
