Folk posting in these forums have noted several times in recent years that after doing a firmware update to older Macs, such as is suggested to prep them for OS X, the machine is no longer able to boot to their original OS 9 Install disk. This usually seems to affect original OS 9 versions older than OS 9.1.
If you can locate a retail OS 9.1 or 9.2.1 Install CD (all retail OS 9 CDs have a white label with a large gold 9), that would probably work.
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As Tom indicated, copying the OS 9 install from your G4 would probably work okay as Classic.
However, if you need to boot the Cube to OS 9 it would probably not work. By default, an OS 9 install is tailored to the hardware on the machine it is installed onto, becoming specific to that model - such are rarely able to boot a different model (with its different hardware).
There may be a solution for that, however - all retail (white label) OS 9 Install CDs can do a Universal Install, which is capable of booting any Mac which can boot to that OS 9 version. Many original Software Install CDs for OS 9 can do the same.
If you have an external hard drive (firewire would be best) available for temporoary use, you could do a Universal Install of OS 9 on it, then copy that to your Cube.
As I recall, the download updaters for OS 9.1 and 9.2.1 can be set to retain the Universal Install configuration of an earlier version OS 9.