I just noticed that my FC cache folder is in the same folder of a specific project.
Can I simply move this cache or erase it and choose a new place for it.
It is on an external drive. Can I keep the cache in my videos folder on my Mac?
You can safely delete the cache if you don't want it as your project will re-create it once you open FCP and that particular project again. When you create a library you have the option of choosing where your cache is stored. See screenshot. If you just manually move it to another folder, FCP won't know where that is, so you need to specify in the storage locations option for the library. You can change this again once it is created, as long as you specify that in FCP.
Generally there is some recommendation to keep your cache on a fast SSD (or faster device) and separate from your library and projects. This workflow varies from user to user and whether you are using external or managed media. Because the cache is written to repeatedly during editing, keeping it separate may have some advantages. If you archive completed projects when you are finished with them, usually you do not want the cache to be part of the archive as it can be regenerated. On our systems, we have one dedicated SSD drive for application cache folders - such as FCP, Divinci Resolve, Logic Pro, etc. We always know where they are and can delete them if we no longer need them, or if they present any type of issue within the respective application. We also do not have to modify every library with a new cache location as most applications will recall your pre-defined storage setting for caches. If you keep it in your project folder, then for each new library you'll have to set a unique path for the cache , otherwise all future cache folders will go to that one project folder, as well as any other projects you create within that same library or any new library.