I haven't used Cubase in a long time, but system 7 sounds about right.
As to the Mac Classic, yes, it has a stripped-down version of system 6.0.3 in ROM, so you can boot off of it. It is not a full 6.0.3, however, so there's no guarantee that a particular program will be able to run.

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Hold down Command-Option-X-O before the happy Mac appears, and you can let go when you get a welcome to Macintosh screen. Now, you can set your start up disk to 'ROM Disk' and when you restart the Classic, you'll notice it boots very quickly! (you don't need to hold the keys if you've set it in start up disk)