If I create a Creative-Commons-licensed work, say CC-BY-SA 4.0, and I include some CC0/public domain content:
If a work is in the public domain, then you have the right to do just about anything you can think of with it. The CC0 license tries to give you the same rights to the largest extent possible under the applicable law.
Those rights include incorporating the CC0/public domain work in a larger work, which is under a different license, without indicating that some parts are not created by you.
As you don't have to indicate that parts copied from a CC0/public domain source are not by your hand, you also don't have to indicate which content is CC0/public domain.
For all practical purposes, your entire work should be regarded as being under the CC-BY-SA license (or whichever other license you choose), but I would not litigate people who appear to have copied only the content that was under the CC0/in the public domain without following your license. For all you know, they obtained a second copy of that content under the original terms.
