How can I get the Google cache age of any URL or web page?

You'll need to scrape the resulting page, but you can view the most recent cache page using this URL:

http://webcache.googleusercontent.com/search?q=cache:www.something.com/path

Google information is put in the first div in the body tag.

Use the URL

https://webcache.googleusercontent.com/search?q=cache:<your url without "http://">

Example:

https://webcache.googleusercontent.com/search?q=cache:stackoverflow.com

It contains a header like this:

This is Google's cache of https://stackoverflow.com/. It is a snapshot of the page as it appeared on 21 Aug 2012 11:33:38 GMT. The current page could have changed in the meantime. Learn more
Tip: To quickly find your search term on this page, press Ctrl+F or ⌘+F (Mac) and use the find bar.