As per Akamai -
A content delivery network (CDN) is a group of geographically distributed servers that speed up the delivery of web content by bringing it closer to where users are. Data centers across the globe use caching, a process that temporarily stores copies of files, so that you can access internet content from a web-enabled device or browser more quickly through a server near you. CDNs cache content like web pages, images, and video in proxy servers near to your physical location. This allows you to do things like watch a movie, download software, check your bank balance, post on social media, or make purchases, without having to wait for content to load.
So I am mainly interested in "post on social media"
Will the CDN prefetch a user's social media content (static?) or will it be done at the user's request because prefetching can be costly, complex and wasteful?
Prefetching generic static information, such as a website's landing page image, a viral video, product images (amazon must use CDN to deliver images for their products else it will take lot of time to load images and will be a very bad experience) makes sense.
Whether it is social media content or a static website, content is not fetched by Akamai except when a request comes to the platform for the content. At that point, depending on how the platform is configured for your particular site, the content is cached for later users for a period of time.
A few notes: