Both Dropbox and Google Drive make it difficult to directly host files.
Dropbox refuses to give you a direct link anymore, forcing you to their preview page, which will not preview many types of files. It wouldn't even preview HTML files.
Google Drive pushes you into "preview hell" as well, also forcing you to download the file if the previewer can't display it.
There is no way to make these services offer a direct link that would ask the browser to handle it. At best you can only get a download link, which will force a download instead of attempting to display in the browser.
Dropbox just made this change, destroying "dropboxusercontent" links, and it affected several of my links on this blog, as well as some automatic tasks I had set up with Zapier.
I was able to save my bacon by using Google Sites. You can use the "File Cabinet" page type for non-html or just create a new web page and paste in the html for your html stuff.
One of these days I'm just going to have to get my own web server. Except then you have to pay for bandwidth.