Yes, it is achievable. Connect the X3 Live to your computer via USB, launch Cubase, and configure Cubase to use the X3 and its ASIO driver as your audio input/output device. Turn OFF monitoring in Cubase. The X3 is your soundcard, and you must connect your speakers or headphones to the X3 outputs to hear the sound from Cubase.

Select your X3 patch and arm a track in Cubase for recording. In Cubase, select the Record Input option for the track - the signal you wish to record from the X3. There are several options. You want to choose the dry (unprocessed) signal for either Tone 1 or Tone 2 - they should be the last two options in the list. Now start playing and recording. You will hear the wet (processed) signal coming through the X3 speakers/headphones, but Cubase will be recording the dry signal which it is receiving from the X3  via usb.