Yes. Both as a app on the Android TV device or via casting it.

I hope you've read the side bar because this subreddit is about Android TV and not cheap imported settops loaded with the Android smartphone OS (avoid these, you will have a bad time).

Recommended official Android TV boxes include: Nexus Player, Mi Box (coming soon), and Nvidia Shield (best).

Duh? If YouTube doesn't work on a Google OS then something is very wrong.

Now I'll go ahead and assume that when you say "android tv box", you're not actually talking about a box that runs the Android TV platform. I think anyone that actually knows the difference between an Android TV device and a TV box that runs the touchscreen-optimized Android OS would be able to google "youtube android tv" and get an answer.

I think you're asking about a hacked TV box that runs some build from AOSP of the Android OS that was designed for handheld devices (and not televisions). In that case, this is not the correct sub to discuss those boxes. You want /r/settopboxes or /r/AndroidSetTopBox. In here, we talk about Android TV, the official OS of the living room from Google, not Android which was made for phones and tablets. And we especially don't deal with some random Chinese dev compiling an AOSP build and installing a handful of illegal streaming services on sketchy hardware.

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