what do they feed on?
The cougar will eat any animal it can catch, from insects to large ungulates : horses, fallow deer, caribou, mountain goat, coyote, American badger and pronghorn.
Cougar
 the cougar will eat any animal it can catch, from insects to large ungulates (over ). Like other cats, it is an obligate carnivore, meaning it must feed on meat to survive. The mean weight of vertebrate prey (MWVP) that pumas attack increases with the puma's body weight; in general, MWVP is lower in areas closer to the equator. Its most important prey species are various deer species, particularly in North America; mule deer, white-tailed deer, elk, and even bull moose are taken. Other species taken include the bighorn and Dall's sheep, horses, fallow deer, caribou, mountain goat, coyote, American badger and pronghorn. 
what is the difference between puma cougar and mountain lion In the United States and Canada, it is also called "mountain lion" where can you find it? America,  In the Santa Ana Mountains what sort of places does it live in? It prefers steep canyons, escarpments, rim rocks, and dense brush. how did it get it's name? The word 'cougar' is borrowed from the Portuguese "çuçuarana", via French; it was originally derived from the Tupi language.
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Cougar [SEP] Hunting and diet
In Pacific Rim National Park Reserve, scat samples showed raccoons to make up 28% of the cougar's diet, harbor seals and blacktail deer 24% each, North American river otters 10%, California sea lion 7%, and American mink 4%; the remaining 3% were unidentified. In the Central and South American cougar range, the ratio of deer in the diet declines. Small to mid-sized mammals are preferred, including large rodents such as the capybara. Ungulates accounted for only 35% of prey items in one survey, about half that of North America. Competition with the larger jaguar in South America has been suggested for the decline in the size of prey items.