Is it possible to connect the Amazon Fire tv cube to Ps4?

I would like to order a Fire Tv cube and wonder if I could connect it with a Ps4 or an Xbox one and then start Netflix on the console

You do not need a Fire Cube for that. If your console is connected to the Internet, you can download the Netflix app and watch it directly from the console.

In the beginning it was possible to use the XBox One To connect a satellite receiver (and theoretically just the Fire Cube or Stick), but this feature is no longer supported.