If you mean recording what the internal sequencer plays in Cubase, it depends on the M3. If the M3 transmits what the sequencer plays via MIDI (not all do), yes. I’m not familiar with the M3, so you need to consult the manual.
You need to set either Cubase or the M3 as master and the other as slave. Now, put a MIDI tracks into Record ready and start recording. When you’re finished, you’ll have a MIDI track with all the channels on it. Select MIDI/Dissolve Part and make sure that Separate Channels is selected. Click OK. Now you will get one MIDI track per channel and you can edit the instruments separately.
Another option is if the M3 comes with any utility to save the sequencer content as a MIDI file. Then you could import (and dissolve, if need be) this into Cubase.
With regard to your other question. In order to hear anything playing through Cubase, you must turn on the monitor button (the one with a little speaker icon on it ii the tracklist or MixConsole). It should be brown. If you still hear nothing, or hear strange phasing sounds, you need to carefully read the section in the manual on setting up MIDI (page 19). Pay special attention to “Setting MIDI Thru and Local On/Off” on page 20.