While doing a back up of our one server, I took a gander at where it was at, and happen to notice that the one account has all these "core" files in it.

(example:  core.123456).

This is with SHOUTcast v1.9 +  icescc.

I took a look at a couple different accounts, using SHOUTcast v1.9 + icescc, but they don't have all those core files in in them.

Anyone know what these files are ?

Those are core dumps, likely from DNAS1 crashing (which it tends to do given that it hasn't been maintained for over 10 years).  Core dumps are a Linux kernel feature; Google "disable linux core dumps" to learn how to turn them off.