Well, for it to be completely deleted, your HDD has to be "demagnetized".

There are some apps that will destroy your files by deleting them multiple times beyond being recoverable. These apps are often described as "File Shredders".

Like a real life shredder, the pieces can still be put together but it would take a massive effort. In your case, it would take hardware to come into play and "do stuff" with your HDD.
So yeah, if you want to get rid of some hot files, use a file shredder.