This is a virtual implementation by the sounds of it. If so, was the allocated disk space fully allocated upon creation? Or was it increased at some point in time? If it was increased, then the appliance would still just be using the originaly allocated amount, as it has no way to reconfigure the disk for increased available disk space.
The delete commands listed by BenDC above are good, but before you delete cores you may want to list them with the command line command:
list --cores
If you get a list of cores, then deleting them will definitely clear up space (they can be bigger than 3GB in size). However, you may want to leave them and call support to investigate why processes are crashing (which creates the core files).