What do you mean ‘occupy space’?
Say we have a perfectly mirrored room. If we fill it with water, we can only put so much water in the room. The room is ‘full’. There is a finite number of atoms that will fit. Instead, if we fill the room with light (photons) how much can we put in? There is no limit.
(… well until the electromagnetic field strength is so high we get electron-positron pair production. What happens then I have no idea, but probably the walls of the room have exploded.)
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