What are the implications of placing the left menu all the way to the left side of the screen vs placing it more towards the center of the screen?
Does anyone know of the pros and cons with these solutions?
About the updated question:
As far as I know, Youtube is using Material design guidelines. In it the navigation drawer toolbar (sidebar) is pinned to the edge of the screen and it might or not be toggled.
In this case, the left sidebar is used for the page navigation, while a right sidebar is used for content related elements (this can bee seen when viewing a single video).
The Facebook example uses the rule for the edge sidebar in the right one.
There is probably not "best position for the sidebar" but I would say a sidebar that is not next to the content may refer to the page or a content different to the actual page one, and a sidebar just next to the main content may refer to elements that are more specific and relevant to the current content.
Both menus are on the left of the content area.
The main difference is that in the Youtube example the content area occupies the whole width of the screen, while the Facebook one has a maximum width and is centered. So in both cases the rule is to set the sidebar (menu) on the left of the content, just next to it.
When to use content that occupies the full width and when set a maximum width is a question that was asked here (implicitly), you might want to check it.
This is less about left-aligned vs. left of content, but more about difference in implementation of responsive layout.
Although Youtube's left nav is left aligned, it is never far away from the main content in the center. If you increase width of your browser, number of video columns goes up to fill up gutter space. But because thumbnail size remains fixed, the width of gutter space varies.
(If you have large screen and always view your browser in full screen mode, then the gutter space will be bigger. In small resolution, the left nav collapses, but youtube provided redundant pill navigation towards the top.)
Facebook on the other hand, has fixed-width main content. Hence, they had no choice but to position it where it is. Otherwise, the left nav would be so far away from the main content on larger displays.
So the short answer is, left nav should be accessible in the context of the main content. Both Facebook and Youtube fulfill this requirement, but using two different implementations.