From looking at the back end of my CGN3, connections with 1 Gb/s interface are indicated with the yellow LED. So, if you have green LEDs flashing that would indicate a 10/100 Mbps interface. This has actually come up for discussion before and it appears that the CGN3 LEDs are reversed from industry standard. The 10/100 Mbps interface is also problematic due to the bug in the CGN3 which throttles down the actual data rate to something between 30 to 40 Mbps. For something like an Xbox, I suspect that it won't be noticeable, but be aware of the reduced data rate.
For the Xbox 360 (?), maybe someone with a CGN3 and Xbox can confirm this, but a quick check online indicates a static IP address and possibly port forwarding to solve the Xbox NAT problem.
However, for now, try the following settings for the CGN3:
1. Under Basic.....Gateway Function....Enable the UPNP. Be aware that this enables applications to change router settings that you may not be aware or, or agree with, however, the Xbox 360 appears to need this.
2. Under Basic.....Port Triggering.....Enable Port Triggering and set the Application name to Xbox LIVE. Trigger the following ports:
- Port 88 (UDP)
- Port 3074 (UDP and TCP)
- Port 53 (UDP and TCP)
- Port 80 (TCP)
3. Under Security.....Firewall...Set the Firewall to minimum.
Save the settings and reboot the router.
Here's the reference to this change:
http://www.pcworld.com/article/242961/how_to_open_up_nat_settings_on_your_xbox_360.html
Note that I haven't recommended Port Forwarding as indicated in the ref as you would have to set a static address for the Xbox. Possibly the Port Triggerng will do the job without having to set a static address and set up Port Forwarding. Running a test after the reboot will determine if its successful.
Here's a Youtube link that appears to solve the issue for the Xbox One :
https://www.youtube.com/watch?v=ZxCjScH9xNc
Continuing with the Xbox One, here is the Microsoft page that refers to what occurs in the Youtube video.
http://support.xbox.com/en-US/xbox-one/networking/nat-error-solution
Follow that page, starting below the DMZ info. Do not set up a DMZ. From reading the Microsoft instructions, it would appear that running a Test multiplayer connection the second time around changes the Xbox Nat type from Restricted to Open.