Uh oh, that does not sound good mate. Could be a head gasket.
If you are going through that much coolant without any visible leaks, it could be ending up in your oil (Cracked cyclinder wall, water jacket, etc.). I went through this issue with a V6 Chev Cavalier.
Just drain your oil. If it looks like chocolate milk (creamy brown colour) then you have an internal coolant leak somewhere and it is getting into your oil. You can also try taking the oil filler cap off from the valve cover and if it has gunky, choco milk looking stuff up in the cap, you have fluid in the oil. Not good news if you do I'm affraid. If it's a minor leak into the oil, you will see droplets of coolant in or on the oil's surface (as we all know water and oil don't mix).
The source of my leaking was a cracked cylinder wall in the #1 cylinder and I had to buy a refurbished short block and rebuild/swap the engine out. Sounds like yous may be leaking elsewhere because if it is a leak in the cylinder wall(s), you will end up burning some of the coolant, which will produce a light, white smoke from your exhaust in which you can smell the "sweet" smell of the coolant.
To help diagnose if it's the head gasket, you might want to do a compression check/test with a compression guage on each cylinder to see if you're losing any compression.
If there is no coolant in your oil, then it must be burning off (in cylinder(s)) as it has to be going somewhere.
Another posiblity is that your rad is boling it all over? Could be a seized water pump or broken thermostat (not opening). What happens if you fill up the coolant and just let you car run/idle in the driveway for 30min? Does the rad boil over and coolant bubbles up and out of the rad overflow?