You'll need a program that can "wipe unused space" on the drive. There are free programs like
Eraser and commercial ones like
R-Wipe&Clean. If it's a big drive with a lot of free space then R-Wipe should be much faster and you could install it as 15day trial. One of the simplest wiping modes would be enough to make sure that simple recovery software won't be able to resurrect the files. If the previously deleted data is more sensitive and you fear that the system may get stolen, then the 3pass US DoD mode or higher may be recommendable but will also take a lot longer.