Note: In 2024, Google completely removed the cache feature, so you obviously can't save cached pages anymore. However, the following information from when the feature did exist may have some historical value.
For whatever reason, I've gotten mixed results with Archive.org. In the distant past, I thought I was able to save cached pages there, but more recently it said that the site was overloaded and to try again in 600 minutes.
On the other hand, Archive.today has worked reliably for cached pages. For example, https://archive.ph/x65wT is the archived version of the cache of SQL sanitizing in code with no user input.