Sounds like you've already reformatted the HDD (i.e., so no files "appear" to exist); so now if you run Eraser to erase the unused (free) space on the external drive, any files that may still actually exist will be securely overwritten. This
post in the FAQ section provides an excellent step-by-step overview. In particular, see the sections entitled
"Erasing the Free Space on the drive" and
"Erasing a complete (non-system) drive".
An alternative approach would be to use
DBAN on the drive, which will overwrite everything on the drive whether or not you have already reformatted. See this
post for more details on DBAN (or see the
DBAN section of the Eraser forum).
(You can burn DBAN to to a LiveCD and boot your computer from the LiveCD to automatically wipe any HDDs DBAN can detect. I haven't used it for external USB HDDs, but several user reports in the DBAN
forum at SourceForge clearly indicate
DBAN detected and unintentionally wiped external USB HDDs users forgot were still connected when they DBAN. In your case, DBAN would do the same for any internal HDDs in the computer, so if you decide to use it to wipe an external HDD, you should
FIRST DISCONNECT ANY INTERNAL DRIVES YOU DO NOT WANT TO WIPE. I believe the external drive will also have to be repartitioned after using DBAN before it can be used again.)
Hope that helps!