I just added a rule to my local iptables to block outgoing UDP packet on port 53 and I get the same error as you. I then removed this rule and blocked the port on my firewall and I got the same result again which is expected.
To answer your question, you need to use your network and system administration skills to work out the route that packets traverse through your network and then check the relevant iptables/firewall rules on each router/host to figure out which one is blocking your requests.
I don't think there is a shortcut to doing this.
use the +trace flag
+[no]trace
Toggle tracing of the delegation path from the root name servers
for the name being looked up. Tracing is disabled by default.
When tracing is enabled, dig makes iterative queries to resolve
the name being looked up. It will follow referrals from the root
servers, showing the answer from each server that was used to
resolve the lookup.
dig +trace @8.8.8.8 stackoverflow.com
; <<>> DiG 9.3.6-P1-RedHat-9.3.6-20.P1.el5_8.1 <<>> +trace @8.8.8.8 stackoverflow.com
; (1 server found)
;; global options: printcmd
. 24299 IN NS a.root-servers.net.
. 24299 IN NS b.root-servers.net.
. 24299 IN NS c.root-servers.net.
. 24299 IN NS d.root-servers.net.
. 24299 IN NS e.root-servers.net.
. 24299 IN NS f.root-servers.net.
. 24299 IN NS g.root-servers.net.
. 24299 IN NS h.root-servers.net.
. 24299 IN NS i.root-servers.net.
. 24299 IN NS j.root-servers.net.
. 24299 IN NS k.root-servers.net.
. 24299 IN NS l.root-servers.net.
. 24299 IN NS m.root-servers.net.
;; Received 228 bytes from 8.8.8.8#53(8.8.8.8) in 35 ms
com. 172800 IN NS a.gtld-servers.net.
com. 172800 IN NS b.gtld-servers.net.
com. 172800 IN NS c.gtld-servers.net.
com. 172800 IN NS d.gtld-servers.net.
com. 172800 IN NS e.gtld-servers.net.
com. 172800 IN NS f.gtld-servers.net.
com. 172800 IN NS g.gtld-servers.net.
com. 172800 IN NS h.gtld-servers.net.
com. 172800 IN NS i.gtld-servers.net.
com. 172800 IN NS j.gtld-servers.net.
com. 172800 IN NS k.gtld-servers.net.
com. 172800 IN NS l.gtld-servers.net.
com. 172800 IN NS m.gtld-servers.net.
;; Received 507 bytes from 198.41.0.4#53(a.root-servers.net) in 351 ms
stackoverflow.com. 172800 IN NS ns1.serverfault.com.
stackoverflow.com. 172800 IN NS ns2.serverfault.com.
stackoverflow.com. 172800 IN NS ns3.serverfault.com.
;; Received 149 bytes from 192.5.6.30#53(a.gtld-servers.net) in 184 ms
stackoverflow.com. 3600 IN A 64.34.119.12
stackoverflow.com. 3600 IN NS ns3.serverfault.com.
stackoverflow.com. 3600 IN NS ns1.serverfault.com.
stackoverflow.com. 3600 IN NS ns2.serverfault.com.
;; Received 165 bytes from 64.34.119.33#53(ns1.serverfault.com) in 102 ms