The STM32CubeMX tool is written in portable java, but unfortunately it is distributed as a Windows executable embedded in a Windows installer.
To install it on Linux:
sudo java -jar SetupSTM32CubeMX-4.11.0.exe- install the tool somewhere in your home, eg:
/home/you/stm32/cubemx sudo chown -R you:you /home/you/stm32/cubemx
To run it:
java -jar /home/you/stm32/cubemx/STM32CubeMX.exe- or mark that file as executable, rename it to
STM32CubeMX.jar, and double click it

As of version 6.2.1, the provided Linux installation package on ST's website is designed for and tested on 64-bit systems, and (from what I gather) works only on a 64-bit system (sorta redundant to state, since ubuntu 20.04 only comes in 64-bit). And yes, no need for JDK, it is bundled with the package.