What the title says, thanks!
Like with all such questions, the sad (but true) answer is “there is no such thing as a perfect mirror ball”, because thermodynamics is a bitch like that. Light goes bounce bounce, ball heats up, your experiment ends – like life, the universe and everything – with some waste heat, slowly dispersing.
You didn’t specify if the experimenter is inside the ball. If yes, the experimenter gets to party first.
It gets absorbed in microseconds. There is no such thing as a perfect mirror, 95-98% reflectivity for the best ones. So it’s all turned to heat in a few hundred bounces which, at the speed of light, only takes a fraction of a second.
The ball gets heavier.
If you find a way to introduce photons inside a ball of perfect mirrors, like you teleport them in or something, and there’s a perfect vacuum inside the ball, they’ll bounce around forever.
That’s because the light inside will behave as a gas, called photon gas ([https://en.wikipedia.org/wiki/Photon_gas](https://en.wikipedia.org/wiki/Photon_gas)) and has pressure, temperature, the whole shebang. The added weight equals the energy of the photons, which will be very little. But its weight will defo increase. I swear I’m not… gaslighting you.
If you keep teleporting light in it, the temperature and pressure will increase until it reaches the melting point (or the breaking point, whichever first) of the material the ball is made of. Then it’ll crack and release the light inside all at once, which should be quite a flash.
Since we’re already in wonderland, with the perfect mirrors and perfect vacuum and teleporting light, we could add that the ball never melts and is unbreakable and perfectly insulating.
Then you can keep teleporting light in it, and you’ll start noticing it gets noticeably heavier.
You can’t do that indefinitely though. At some point, it’ll turn into a black hole.
Others have answered your question. To add a fun idea you can also create an incredibly powerful explosion using mirrors, light, and a black hole.
The light bounces around, losing energy with each reflection, until it completely dissipates. It looks a bit like this: