I was depressed at the time, so I chugged three glasses of beer.
Three cups of liquid is three cups of liquid, or more simply, three cups.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well. Just watch out for 杯, which becomes ばい thanks to our old friend rendaku.