I got a pair of winter white hamster, male and female.
The female always sleep in her cage, but when i let her out of the cage,
she runs like mad. She even runs non-stop in the exercise ball.
But once i put her back in the cage, she just lay down quietly again.
I know she like the ball very much, but why she feel depressed once go into her cage?

I doubt she's depressed. It's probably because when you let her out she's just excited what with the exercise ball and what not. When you put her back she probably feels a bit safer in the cage and calms down. Hamsters are quite nervous animals so she probably feels safer in the cage hence why she goes quiet.

shes not depressed. she just thinks, k, playtime is over, time to settle down and go to bed.
hamsters like to play, and play, and play, nad play, and guess what...PLAY!
so when she goes in her cage, she thinks, man, the playime is over, i was just gettin started.