Fetching details from the dictionary...

one cup (of); one glass (of); one bowl (of); cupful; glassful; bowlful; spoonful
one drink (of alcohol)
full; filled (with); brimming (with); crowded; packed
fully; to capacity; to the maximum; as much as possible
a lot; much; many
all of ...; the entire ...
one (squid, octopus, crab, etc.)
one (boat)
グラスにいっぱい水を注いだ。
I filled the glass with water.
部屋は荷物でいっぱいだ。
The room is full of luggage.
お花見の公園は人でいっぱいだった。
The park for cherry blossom viewing was packed.