Suppose you fill a glass with ice cubes .when the ice cubes melt, is the glass still full ?

Well, you can't "fill" the glass with ice cubes to begin with.
The ice cubes never fit together perfectly, and there are always
a lot of air-spaces between them.  When the ice melts, there is
almost exactly the same amount of air in the glass as there was
originally. (Actually, a tiny bit more, for other reasons.)