Can I back up my iphone using itunes on a mac book with big sur?

iTunes cannot be installed on a Mac running Big Sur. It was discontinued and replaced with other apps. See: What happened to iTunes? - Apple Support

To backup an iPhone on a Mac running Big Sur, Finder is used instead of iTunes. See: How to back up your iPhone, iPad, and iPod touch with your Mac - Apple Support

Iphone/iPad management has been moved from Music/iTunes to the Finder

Connect the iDevice to the Mac with a lightning to USB/USBc cable

Open a Finder window

Look in the side panel under locations

Your iDevice name will show up in the list

Click on it and the configurator panel previously in iTunes will launch

Under general you will find various options for backing up your iDevice including to your Mac