Can't get rid of www.googleapis.com cookie.

I regularly flush cookies out of my system with CCleaner, but it doesn't get rid of this one.

What can I do to erase it from my PC?

You haven't said which browser you are using so I can only post a link to How To Geek which discusses this very topic.
https://www.howtogeek.com/111925/del...rs-in-windows/

Thank you Tpau

I'm using Chrome. That article shows screenshots from a different version of Chrome.

I've added the url to the Block facility in my Chrome settings. I can't see how to add a screenshot in this forum.

Blocking that url hasn't made any difference. The cookie is still on the PC somewhere.

I copied the following text from Google Chrome Help, it should fix your problem but some cookies can be stubborn little buggers and if that's the case here you might need someone a bit more knowledgeable to help you remove it.

"Clear all cookies
If you remove cookies, you'll be signed out of websites and your saved preferences could be deleted.
1.On your computer, open Chrome.
2.At the top right, click More More and then Settings.
3.At the bottom, click Advanced.
4.Under "Privacy and security," click Content settings.
5.Click Cookies.
6.Under "All cookies and site data," click Remove all.
7.Confirm by clicking Clear all."

"Delete specific cookies
1.On your computer, open Chrome.
2.At the top right, click More and then Settings.
3.At the bottom, click Advanced.
4.Under "Privacy and security," click Content settings.
5.Click Cookies.
6.Under "All cookies and site data," search for the website's name.
7.To the right of the site, click Remove."

Tpau said:

I copied the following text from Google Chrome Help, it should fix your problem but some cookies can be stubborn little buggers and if that's the case here you might need someone a bit more knowledgeable to help you remove it.

"Clear all cookies
If you remove cookies, you'll be signed out of websites and your saved preferences could be deleted.
1.On your computer, open Chrome.
2.At the top right, click More More and then Settings.
3.At the bottom, click Advanced.
4.Under "Privacy and security," click Content settings.
5.Click Cookies.
6.Under "All cookies and site data," click Remove all.
7.Confirm by clicking Clear all."

"Delete specific cookies
1.On your computer, open Chrome.
2.At the top right, click More and then Settings.
3.At the bottom, click Advanced.
4.Under "Privacy and security," click Content settings.
5.Click Cookies.
6.Under "All cookies and site data," search for the website's name.
7.To the right of the site, click Remove."

Thank you again Tpau.

Excuse the delay, I've had to attend to a couple of things which needed to be done in the house.

Before reading your reply I had already done most of the things you recommend. I didn't find the website's name anywhere.
I then ran a rootkit hunter and Avast's browser cleaner, and then checked CCleaner. The cookie had gone; I don't know which operation moved it.

I appreciate your time, thank you.