Can a router be configured from outside the local network?

My router can be configured by going to when connected either by WiFi or by Ethernet cable.
Can the same configuration web interface be accessed from the external interface (the public IP of the router)?

Some background:
I have a “Technicolor TD5130” and I wanted to change the default password that the ISP preconfigures. But even after changing the password, the default weak password for some weird reason still works. So I’m wondering if someone can access the router configuration if they can’t initially connect to the router through Ethernet nor WiFi.

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Author: RationalFragile