Can I connect Echo dot Generation 3 to the ps4 with a cable?
Unfortunately not possible, the Echo Dot only has one output, i.e. You could connect it to a stereo system to turn it into a smart stereo system or to stream music.
You can use the echo dot as a bluetooth speaker for your ps4. However, this is rather unsuitable for gaming because of the delay.
You can't connect the echo dot by cable, as this is only for the power supply.
No, the Echo dot (or Google Bot etc) only have one output port, so you can connect the Echo dot to loudspeakers and thus hear the voice of Alexa via loudspeakers, but you can't connect any devices to the Echo Dot and use the Echo Dot as a loudspeaker You can, for example, run Spotify over the Echo Dot via Bluetooth (I don't know if it is also possible via the PS4, I'm a PC gamer) but you can't run games and other media via Bluetooth over an Echo Dot