Night Stalker by Sally Maxwell. "All of the cheetahs I've seen are in preserves in South Africa, so I have not been able to view their true nature.
A cub falls down a cliff and calls for help. The mother loin calls the other lionesses to help her. They try but are too afraid to venture down the cliff. The mother lion than gets the courage to go down the cliff to rescue her cub. Never doubt the power of a mother's love.
Baby racoons will do this when they are happy and feel like they are protected and safe. I've had several litters of baby racoons and they would always purr when they were curled up in a warm spot, nursing or when we'd pet them.