Can a router be cleaned or formated?

I got banned in a fun forum for defending myself from a psychotic stalker, who seemed to be hellbent on starting flame wars with me. The monster follows me everywhere. All I did was copy and paste his ugly post, and posted it back at him as the reply to his abusive post, and I got "banned for insulting a member".

I needed some data from that forum, but I couldn't get in. Seemed my IP was also blocked, so I disconnected the router, connected straight to the modem, rebooted the tower and the modem, showed a new IP, got into the forum, and collected the wanted data.

So it seems that the router holds old IP's data.
Is there a way to clean out or format a router, to erase the old IP's it holds?

Not the router but the modem. The cable modem know what is connected to it. via the MAC. If you want a new IP Address you just have to reset the router and it should get a new IP Address.

Most routers have an IP release/renew capability, or disconnect/reconnect. That should force your ISP's DHCP server to assign you a new IP address.