Unless your Spectrum cable box, TV, and/or AVR are highly unusual, the LAN port cannot be used how you're describing. That's just for a network connection. For the audio/video, your only real option is to use HDMI. If your cable box actually supports video/audio out of the RF port, that's almost certainly highly limited in terms of the audio/video you can get out of it. It's only really (rarely) used for picking up OTA transmissions, and that would just be the RF port on the TV.
As an aside, why is your entire post in code formatting?