Hey @melanie1112, thanks for reaching out to the Dropbox Community!
I had never tested this out myself, however, here's a list of file types that can be previewed through the Dropbox mobile app for iOS.
Even though you can't preview it directly through the Dropbox app, you should be able to open it with any e-reader you might have installed.
Alternatively, you can also go to dropbox.com and convert your .epub files to .pdf, .png or .jpg, so that you can preview them.
I hope this helps, but let me know if you have any questions.