Power down Apple tv box

From the linked support document:

Put your Apple TV to sleep

After a period of inactivity, your Apple TV automatically goes to sleep. You can also put your Apple TV to sleep with your remote or from Settings:

• Apple TV 4K or Apple TV HD: With your Siri Remote or Apple TV Remote,* press and hold Home  for three seconds to bring up Control Center, then select Sleep . Or select Sleep Now in Settings.

• Apple TV (3rd generation and earlier): With your Apple Remote (aluminum or white), press and hold Play/Pause  for five seconds. Or select Sleep Now in Settings.

To wake your Apple TV, press Menu or Home  on your remote.

For an online user guide, see: Apple TV User Guide - Apple Support

The sleep command will put it in standby mode. To really turn it off, you have to disconnect the power cord.

How to turn off or restart your Apple TV - Apple Support