I have the Asus RT-N56U router. How do I find out if the router supports POE? A Google search for "asus rt-n56u power over ethernet" did not produce any meaningful results: http://goo.gl/qqNFm
Also do all routers support POE?
The specifications do not list PoE so this device does not support PoE. Most routers will not support PoE.
I would guess more switches support PoE than routers
You can add a PoE injector to most networks that will allow you to connect a device that requires PoE to a switch or router without PoE. One example is the HP 1-port Power Injector (J9407B)