I don't use the UR22, but just trying to help shed some light here....No, I wasn't saying the USB shouldn't work, it should. I was saying that most people deactivate their motherboards on-board audio (I do this in the BIOS), I also double check in my 'Devices' to make sure my ASUS mobo's on-board audio is deactivated. The only sound card I have activated on my computer is my professional audio interface, the one meant for studio recording. I also deactivate any and all Windows sounds (I mean the beeps and such).
Then I was saying that when you're using Cubase, (after deactivating on-board audio - your Realtek) you should only have available your UR22 audio interface to select from as your ASIO I/O device. It sounded to me like you were trying to use your UR22 AND your on-board Realtek audio...maybe I misunderstood. You should have your 'powered' speaker monitors connected to your UR22 L/R Line Output (I thought you said you had them connected your speakers to your on-board Realtek, don't) Line outputs aren't enough to power passive speakers properly, though the headphone output should be blasting from the UR22.
After doing the above, see if your UR22 can then be selected within Cubase as your ASIO device (it has to be in order to work)...it may or may not do the trick, but your do not need your Realtek now that you have a proper interface anyway, nor do you need Windows sounds on a recording machine.
Again, I was saying that I've read many people having trouble getting audio I/0 of their interface when using a USB audio interface...NOT all, or that it can't be done, it CAN be. I've tried a USB interface myself before and I had trouble getting it reliably recognized...only sometimes it would work.
What is wrong, if it's defective, or what you're doing wrong (if that's the case) I'm not sure. Try the deactivation of on-board audio 1st, you should anyway imo. Delete & reinstall drivers if you have to. Maybe something is incompatible with the UR22 and your computer.
Have you checked, or can you check your UR22 software control panel for levels & routing? Within Cubase's VST Inputs (or VST Connections) you should have your I/O's selected, then within Cubase's Arrange Window (Project Window), next to each track lane to the left column, you should also have the corresponding I/O set.