When you first activated your SB8200 with you service provider,  they subscribed an IP Address to send the signal. The SB8200 is just a cable modem, so the IP Address that they subscribed only works with one ethernet port. In order for you to use the second ethernet port,  you would then have to subscribe a second IP Address with your service provider however not all the service providers offer a second IP Address for residential service. 
My best recommendation is to connect a Wi Fi router into the first ethernet port on your SB8200 and any other wire connection that you need to do, place it into the back of the Wi Fi router.

Hope this could help you.
 

Hi,

That's a good question, the SB8200 is a cable modem and does not support ethernet segregation. You can only connect one IP address to the modem. I would recommend to connect cable modem (from port 1)directly to a router . If incase the user wants to connect multiple ethernets connections , please recommend user to use switch.

Hope this is helpful.

Also, something that was not mentoned is that the SB8200 has link aggregation. This allow customers to combine those ethernet ports into one we can say for routers that also have link aggregation to achieve speeds up to 2 Gbps.

You can go to this link to find further information.

http://arris.force.com/consumers/articles/General_FAQs/SB8200-Link-Aggregation-Setup