Blog Archive on Single.php

I’m trying to get the “archive” dropdown to work on my sidebar on my single.php.
I have copied and pasted from the source code into my sidebar, so the archive and recent posts are there, but they won’t be updated automatically because the code was static… Where do I find the dynamic code for loading that information?

It’s a customer sidebar made with a widget, but the widget won’t load on single.php for some reason… If we can get that to work instead, that would also be useful… Any thoughts?

The website is beta.cleantelligent.com/blog