I've never used the zoom unit in question, and haven't touched Cubase in years, but I may be able to help.
AFAIK, I belive that the ASIO driver system can only access one device at a time, so you won't be able to use the zoom as the input device and the soundblaster for output.
The Zoom is effectively being used as an external sound card. So you need to choose the Zoom's ASIO driver from within Cubase. This should then route Cubases output to the zoom too, which should also give you live monitoring. So you'll need plug the zoom into your speaker or use headphones. It may be worth investing in a small mixer so you can keep the zoom and soundblaster routed to your speakers.
You shouldn't need to change the default sound card in the windows control panel, Cubase should overide this. So you should be able to leave this as the Sounblaster.
If you have choices of input as described, it sound to me like you have the Soundblaster ASIO active in Cubase. Although I don't know what the zooms choices will be.
There is a full pdf manul on zoom's website that has a walkthough of how to set it all up.