does it have any reference in mythology?
The Inca city of Cusco is reported to have been designed in the shape of a cougar, and the animal also gave its name to both Inca regions and people. The sky and thunder god of the Inca, Viracocha, has been associated with the animal.
Cougar
The grace and power of the cougar have been widely admired in the cultures of the indigenous peoples of the Americas. The Inca city of Cusco is reported to have been designed in the shape of a cougar, and the animal also gave its name to both Inca regions and people. The Moche people represented the puma often in their ceramics. The sky and thunder god of the Inca, Viracocha, has been associated with the animal.

In North America, mythological descriptions of the cougar have appeared in the stories of the Hocąk language ("Ho-Chunk" or "Winnebago") of Wisconsin and Illinois and the Cheyenne, amongst others. 
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. 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. what kind of animal is the last mentioned one? It is a species of artiodactyl, often known colloquially in North America as the American antelope does it's predator faces any threat? Yes, by habitat loss, habitat fragmentation, poaching, heavy traffic, which causes frequent fatal accidents how is it conserved? It is  listed as least concern on the IUCN Red List.
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Cougar [SEP] In mythology
The grace and power of the cougar have been widely admired in the cultures of the indigenous peoples of the Americas. The Inca city of Cusco is reported to have been designed in the shape of a cougar, and the animal also gave its name to both Inca regions and people. The Moche people represented the puma often in their ceramics. The sky and thunder god of the Inca, Viracocha, has been associated with the animal. In North America, mythological descriptions of the cougar have appeared in the stories of the Hocąk language ("Ho-Chunk" or "Winnebago") of Wisconsin and Illinois and the Cheyenne, amongst others.