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Fusion 360 stores data primarily in the cloud. However, a local cache is generated to speed up access to frequently used files.
If you are searching
Autodesk does not aggressively advertise the full offline installer on the main product page, but it is available through their Education or Trial community pages (often labeled as "Browser Download" or "Download Now" vs. "Install Now"). autodesk fusion 360 full install version
To find it legitimately: