I had to check recently what is the storage capacity of an Apple TV 3rd generation device identified as model Apple TV A1469. Strangely NOWHERE in the About and Settings is shown the capacity. It seems that officially for this device there is no storage available and stated!!!

Apple TV (3rd Generation, Early 2013) Specs
Identifiers: 3rd Gen – MD199LL/A – AppleTV3,2 – A1469 – 2633

Apple TV (3rd Generation) has 512 MB of RAM and is capable of supporting 1080p video.

Processor Speed: 1 GHz* Processor Type: Apple A5

Apple does not specify the amount of RAM onboard. However, by third-parties it was confirmed that it has 512 MB of RAM.

Standard Storage: 8 GB SSD Storage. Officially, the third generation Apple TV models have no internal storage. However, third-parties have determined that they actually have 8 GB of flash memory to cache content, just like the second generation Apple TV.