If you have a 6 liter that is drinking coolant, you most likely have a bad EGR. Do not continue to drive it, and I wouldn't drive a 6 liter accross the street without a tuner that monitors oil and coolant temperature. Justin in right on with the differential temperatures being critical to plugged coolers on 6 liters.
Here's the short version: egr starts to fail, you start slowly drinking coolant, burning it off via your tailpipe. Green coolant gets low, gets hotter and starts to precipitate the oil cooler plugging "gel". You keep driving it until your cooler is so plugged that it can no longer cool oil effectively. Then you put a load behind it one day and it pushes out a head gasket. Then you pull the cab to replace the head gaskets and start to invent new swear words as your credit card becomes maxxed out at the same instant.
You have to keep an eye on the temperature difference between the oil temp and coolant temp as it is directly related to how clean your oil cooler is on a 6 liter. Go get a tuner and see what the differential is at steady state driving. My buddy's was 30 degrees after only 75K miles, which is way higher than it should be. He caught it and did all the work (about 2K for parts) and his truck is completely bulletproof, with coolant temps within a couple degrees of each other. No headgaskets, great power, great fuel mileage, original head gaskets.
Read the 6 liter blogs and pick your poison, but I'd park it and diagnose/fix it now. The 6 liters can be made very, very bulletproof without pulling the heads off, but you have to fix all the factory gremlins that stack up and make bigger messes.
Good luck.