Normally the simple way that works is to power off your modem & router for a few seconds and power back on, if that doesn't work you might need to open some ports, I think port 21 is the Xbox port.
you would have to login to your modem/router through the web interface and open the ports there. if it is a home network open the run box, type cmd, once the command window opens type "ipconfig" without the "". the default gateway is the ip of your router/modem. most likely 192.168.1.254 or 192.168.1.1 type this in a web browser and the un pw are usually u/n:admin p/wblank) or admin or there might be login credentials on the barcode of your router/modem.
The easiest method is to start with the router model, then go to port forward this will ask you a series of questions as model type and number, then follow information related to the opening of either specific ports for Xbox Live, or using UPnP to automatically open them as needed. I run Netgear routers with DDwrt firmware so mine is slightly different but performs better. If you post your router info i can help you with opening them or you can follow the link above. Good luck P.s. Addz the Xbox ports vary from game to game, but Xbox Live uses 53,80,88,1863,3074 ports. 3074 port is the main to connect with Live, and the others are communication between games and voice. Port 21 is an FTP port
sounds like you are running a cisco router. either way the default gateway should still be the ip of your router.