I'm a little puzzled by the combination of the command you used and the error message you claim. The use of the f option followed by the argument /backup would indicate that you are wanting ufsdump to send its output to the "file" /backup. But, your description indicates that you were intending it to go to another disk, which would imply that /backup is a directory and is the mount point for the other disk/partition. If so, that would be wrong. It should be /backup/todays-backup, where todays-backup is the name of the file you want it to send the backup stream to.

If you tried this a couple of times, once with a directory /dump, and your server were sun1, then I could imagine an error message referring to that. Otherwise, I have trouble figuring out where the "sun1/dump" came from.

Also, the u option will be useless if /var is part of the root partition. /etc/dumpdates is only updated if you backup a complete partition. If you select directories or files within a partition to be backed up, then you get a full backup of those directories or files, and you do not get /etc/dumpdates updated.