Filling holes in trees with cement is not a good idea - in fact, that usually does more harm than good. Yes, tree removal is often an expensive avenue of last resort.
Needless to say, you need an on-site evaluation by a professional tree care specialist (e.g., certified arborist, urban forester, pathologist/entomologist, or horticulturist). Only an on-site consultation can provide you with a legitimate expert opinion.
Contact your local university extension office to see if they can come out and look at your tree. Otherwise, you will have to call a certified arborist (check the yellow pages).
Best of luck!