The control board inside the printers (an Arduino compatible board) just runs Marlin firmware (that’s how it interprets the G-code).
Cura is a “slicer”. It converts the 3D meshed geometry file (typically a “.STL” or “.OBJ”, or “.3FM” file) into G-code so that you can send it to the printer (which is running Marline).
The Arduino in the printer doesn’t have nearly enough memory or processing power to run the Cura slicing software (or any slicing software).
As @Iggy points out… if you want something that can run Cura but don’t want to use a laptop or desktop computer (it will run on Windows, Mac, or Linux) then you can use a Raspberry Pi. I would suggest a Raspberry Pi 4B with 4GB RAM (minimum RAM should be 2GB … I don’t think I’d try to run it on a 1GB Raspberry Pi).
As I check the memory utilization of Cura on my mac… (which is a Unix OS) it’s using about 1.5GB RAM for just that application. I’d expect it to be similar on the Pi (although the Mac is running 64bit … it might be a little smaller on the Pi because that will be 32bit.)