Losing coolant but not leaking

If you are absolutely certain that there isn't any external leaks then it has to be burning it. You may have a head gasket that is leaking slight enough that over time you notice a loss of coolant but it may not leak bad enough to notice it steaming out the tail pipe. Make sure that you do not have an intake manifold leak that just isn't hitting the ground. That is the first place I look for antifreeze leaks on GM engines(If thats all you been looking for is any fluid on the ground beneath where your car sits)