Can I upgrade to Big Sur on my Mac Mini late 2012 2.6 GHZ Quad VCore i-17 8 mb Memory.

No. The most recent version of MacOS your mini is capable of running is Catalina (10.15), which is now 2 versions old. Whilst there is a way of obtaining older versions of MacOS (and I can tell you if you want to install Catalina, but I would strongly recommend buying a new Mac (if you can afford to) as yours is now 9 years old and older systems which can't run the latest version of MacOS (which is Monterey (MacOS 12), by the way, Big Sur was the previous version) are open to security vulnerabilities). 9 years is a good age for a computer.

Sorry, no. See the following from Identify your Mac mini model - Apple Support

Mac mini (Late 2012)

Model Identifier: Macmini6,1; Macmini6,2

Part Numbers: MD387xx/A; MD388xx/A, MD389xx/A

Newest compatible operating system: macOS Catalina 10.15.7

Migrating from Catalina to the current macOS Monterey on a new Mac is relatively straightforward. Also see: Move your content to a new Mac - Apple Support