my Mac has no room to download the MacOS Big Sur , what do I do?

the easiest way would be to buy an external HDD or SSD and move your larger files (videos, pictures, etc...) to it. once there they can be removed from your internal drive to free up that space. you could also read these two pages:

Optimize storage space on your Mac

How to free up storage space on your Mac

What is “Other” storage on a Mac, and how can I clean it out?

Free up storage space on your Mac

OmniDiskSweeper Safe to use

How to delete Time Machine snapshots on your Mac

See used and available storage space on your Mac

The final word from Apple on Managing the " Other " Category

• Other: Contains files that don’t fall into the categories listed here. This category primarily includes files and data used by the system, such as log files, caches, VM files, and other runtime system resources. Also included are temporary files, fonts, app support files, and plug-ins. You can't manage the contents of this category. The contents are managed by macOS, and the category varies in size depending on the current state of your Mac.

The files that you have control over are located in the Documents, Downloads, Pictures, Music and Movies folders.  You can use either of these two free apps, GrandPerspective  or OmniDiscSweeper, to find the largest files on your drive so you can determine if they can be deleted or moved to an external HD for storage.  

Note: you can empty the Downloads folder after the apps and/or updates that were downloaded have been installed or applied.  Many users have found a couple of Gigabytes of files in their Downloads folder which are no longer needed.