You should be able to burn CDs on that system - in fact every Mac mini has shipped with either a CD burner (combo drive) or DVD burner (superdrive). You should not need additional software, since everything necessary is built into MacOS.
Check that the drive is being correctly recognized by going to the Apple menu, selecting About This Mac, then clicking More Info. This launches the system profiler. Then, click the ATA heading on the left, which should then give you details of the drive. Click Disc Burning on the list on the left to see what media types the drive supports, and ensure you are using a compatible blank.