Deleted file from server, still shows in web browser
I uploaded/FTPed an html file (not index.html) to my site's server. Looked at it in a web browser ("http://[website].com/thefile.html") - works ok. Then I made a change to the HTML file, FTPed it, and looked at the should-be-new webpage in a browser and the old version shows. Cleared the browser cache. Still same problem. Tried it in 2 other browsers - still the old version of the HTML file shows. I DELETED the file from the server, and in a browser, the old html/webpage appears! Yes, I cleared the browser cache. I FTPed it again and can edit the server file in FileZilla and I can see that the NEW file IS on the server. Apparently, the browser, when it is connecting to [website].com, is getting the file from some other server, not from [website].com.
I FTPed the file to "sucuriip.[website].com" (not "[website].com") as per GoDaddy instructions given some time ago. What's going on and how do I fix it?
UPDATE: Many hours later, the new HTML file shows in a browser. Could someone please explain, and how do I get that update to propagate faster?