I believe you are looking for the IP between the modem and the ISP, i.e. the external IP of the modem, not the external IP the router (The router is connected to the modem, perhaps in your case its internal). This isn't possible from your computer (traceroute will give you the private address), but you have a couple of choices.
1) Go to your default gateway on a browser and see if the WAN's private/CGN address is there.
2) Call your ISP (If you can get someone to ping your modem, you may have the same success as this guy)
3) Get a cable splitter* (may be illegal, but I mean if you don't go reading your neighbors stuff doesn't really matter, websites will always use https for sensitive information anyway), and then get a modem for that cable to turn it into ethernet, and then sniff that ethernet.
*Make sure the splitter/tap is read-only, and that the write port is plugged into your actual modem / wall cable!
so www.ifconfig.me/ip isn't what you want? – barlop – 2013-06-03T11:17:06.410
Try with traceroute (or hping in traceroute mode). With a bit of luck, you will see an answer from a private IP just before the connection enters the Internet, and that IP will be the one of the outside router. – LSerni – 2013-06-03T11:19:29.983
The router itself doesn't have the IP, A NI of the Router has an IP(and not a switches NI ports). On the LAN side of a home router, is a switch, just one IP 192.168.1.1 On the other side, if it's connected to your ISP it must be a WAN that end.. It's not designed for a LAN to be connected there.
I haven't used more advanced routers though that allow LANs there, but if you're connected to your ISP, it's not designed to have a LAN there. It's meant to either connect straight to the wall(if the socket in your "home router" there is a telephone socket),(cont) – barlop – 2013-06-03T12:35:40.753
or straight to a modem, if the socket is an ethernet/RJ45 socket labelled WAN. – barlop – 2013-06-03T12:36:09.207
I think if it could connect a LAN on that side, then the Router's Administration IP(don't know what NI that'd be associated with), but that's show you the IPs of any port. On a regular home router, you have the switch ports which don't have IPs(the computers on them do). and the other side has an interface which gets an IP, but if it was a more professional router then that interface could be given an IP by the Router, and then, it'd show you what IP it is being given But also, even my home router tells me my internet ip address. If it was sent a private one(theoretically) it'd display that. – barlop – 2013-06-03T12:40:48.990
@barlop : mine is just a home router. here's the scheme : PC-->linksys wireless router-->modem(cable modem)-->provider-->WAN. Since the router doesn't have public IP, i'm thinking there should be private ip involved in between the router/modem and the provider. am i right? – andio – 2013-06-03T13:24:43.367
@lserni : after 192.168.1.1, i just saw * * * , then go straight to WAN . there's no other information. – andio – 2013-06-03T13:26:20.820
@andio I don't know for sure.. is that WAN interface's IP the public ip(then the modem won't have an IP), or the WAN interface 192.168.1.1 (same IP as managing the router) and the modem doesn't have an IP. And if the WAN IP is .1, and the management is .1 how does it work electronically when you access management locally, does it go to the same network interface somehow within the router. If they both use .1 then maybe the management is a kind of virtual network interface sharing an IP with the real one that's the WAN one. I don't know. You ask a thought and question provoking question – barlop – 2013-06-03T16:11:40.503