(A) If you are asking about the router itself, look in the config for one or more command lines like this:
ip name-server x.x.x.x
ip name-server y.y.y.y
where x.x.x.x and y.y.y.y are IP addresses of DNS servers.
(B) If you are asking about identifying what DNS servers are being accessed via your router, you can do that using access-lists and logging. Try these commands (assuming a router with a FastEthernet0/0 LAN port and a Serial0/0 WAN port):
logging buffered 16384 debugging
interface FastEthernet0/0
ip address f.f.f.f 255.255.255.0
ip access-group LAN-IN in
ip access-group LAN-OUT out
interface Serial0/0
ip address s.s.s.s 255.255.255.252
ip access-list extended LAN-IN
remark Log the DNS servers LAN users access which are not on the LAN.
permit udp any any eq domain log
permit tcp any any eq domain log
permit ip any any
ip access-list extended LAN-OUT
remark Log the DNS servers on your LAN which are accessed by users who are not on your LAN.
permit udp any any eq domain log
permit tcp any any eq domain log
permit ip any any
NOTE: "domain" is the well-known name for port 53, which is the port number that DNS uses. If you enter the number 53 after "eq" the router will automatically convert it to "domain".
Run the "show logging" command to see the IP addresses of the DNS servers being accessed. The log messages will tell you which access-list created each entry, the source IP address of who made the DNS request, and the destination IP address of the DNS server.
After you get a sampling of server IP addresses from the log, you should probably just remove the access-lists from the interface, using the commands
interface FastEthernet0/0
no access-group LAN-IN in
no access-group LAN-OUT out
Or you can modify the access-lists to just track hits to those specific servers and log any new ones:
ip access-list extended LAN-IN
remark Log the DNS servers LAN users access which are not on the LAN.
permit udp any host x.x.x.x eq domain
permit tcp any host x.x.x.x eq domain
permit udp any host y.y.y.y eq domain
permit tcp any host y.y.y.y eq domain
permit udp any any eq domain log
permit tcp any any eq domain log
permit ip any any
ip access-list extended LAN-OUT
remark Log the DNS servers on your LAN which are accessed by users who are not on your LAN.
permit udp any host z.z.z.z eq domain
permit tcp any host z.z.z.z eq domain
permit udp any any eq domain log
permit tcp any any eq domain log
permit ip any any
Where x.x.x.x, y.y.y.y, and z.z.z.z are DNS servers you found in your log messages.
*****CAUTION: If your LAN users point to a DNS server on your LAN, and the DNS server on your LAN does all the lookups on behalf of the users, you will see many, many, many log messages!!! One or more for each URL that is resolved to an IP address. All this logging could seriously impact router CPU performance. If you know you have a DNS server on your LAN that your LAN users refer to for lookups, modify the LAN-IN access list so that it starts with permits for tcp and udp from "host d.d.d.d" to "any eq domain" without the "log" parameter.*****
