The short answer is no, you can't share them for free, because it would be a violation of copyright laws. The exception, of course, would be for e-books of content that is already in the public domain, like the titles you would find at Project Guttenberg. Even then, they ask that you acknowledge them if you are reposting their e-books.
An alternative approach might be to encourage authors to provide you with copies of any e-books that they have decided to make "perma-free". Many authors will give away the first book in a series for free in an effort to drum up interest in the hopes that people will like it enough to go and buy the other books in the series. I know many authors are constantly looking for places to promote such titles, and if you set up your site in a way that they find appealing, they will give you all the content you need. It would certainly help if you could explain how you plan to draw in actual readers.