Thanks Pilou.
Sorry for the two boxes (it's an error of me when i prepared the files, in the original, there aren't 2 boxes).

So I tried the union (why union because there is only one object ?) like you say, but this doesn't work too. Or I don't understand all of this.
I have only 2 objects in the new files in attachment ;-)
I would like make the boolean diff in the same objects position than in the files. Nothing occurs.
(in you file, the cube isn't in the same place than the original file)