scenario: router has two interface. gi 0/0 and gi 0/1. gi 0/1 connect to internet with defined default gateway. I can ping default gateway (22.214.171.124) but extended ping from gi 0/0 to default gateway doesn't work. I applied "ip routing" command and also I applied static route to default gateway "ip route 0.0.0.0 0.0.0.0 126.96.36.199" but still not work. therefore all PC behind the router which are connected to gi 0/0, can't connect to internet.
I wonder a little bit about terminology in the original post. It says that the router has a defined default gateway. I am not sure whether that is literal and the router is configured with ip default-gateway or something else. A router will use the default-gateway when the router is operating as an IP host but does not use that address when it is routing packets. But then the original post says that he added ip route 0.0.0.0 0.0.0.0 188.8.131.52 so at that point the router had a valid default route which it would use to route packets, so there must be some other issue.
Since the router can ping the 184.108.40.206 address it demonstrates that the router can forward to that address (this would be true for the standard ping and the extended ping). It suggests that the router at 220.127.116.11 does not have a route to the address on the g0/0 interface. The original post did not have any information about the addressing of interface g0/0. My guess is that the interface has addressing in private address space and that there is no address translation configured. Perhaps alireza can clarify what addressing is used and whether there is any address translation.
Thanks for the additional information. Knowing that there is not any dynamic routing protocol between your router and the provider and knowing that interface g0/1 has a public (provider supplied) address whle inteface g0/0 has private addressing confirms what the problem is. In the extended ping the source address is 192.168.20.1 and the provider has no route to get to that address. The solution is to use NAT - or in your situation probably to use PAT which will translate all addresses on g0/0 using the address on g0/1.
The config might look something like this:
ip nat inside
ip nat outside
access-list 50 permit any
ip nat inside source list 50 interface gi0/1 overload
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