I have a Ion Tape 2 Pc Cassette player, is there any software that would record the cassette as I play it?
Any audio recorder or audio editor should work.
I like Audacity because it gives you a fair amount of control and you can lay down multiple overlapping tracks. You may or may not need that kind of complexity.
The trick to sound recording is to get the levels right on your mixer (and on the other device). You never want it so loud that it clips (goes about -0 dB), but you want it loud enough that it's not too quiet.
It looks like your Tape-2-PC device is plug and play, so it should just appear as an audio device in Ubuntu, alongside your PC's built-in sound card. You'll need to select the correct input device in order to record from it, otherwise it'll just try to record from the Mic/Line-in jack on your computer.