Can I keep my WhatsApp videos on the cloud? My Android smartphone only has 4 GB and the WhatsApp folder already has 500 MB in the WhatsApp Video sub-folder.

I know I can make a one-time back up my WhatsApp data on the cloud but I need a permanent solution like keeping all the videos older than 3 days on the cloud, in order to permanently save my storage space.

Does WhatsApp have such a feature? It should not be very difficult for them to do that because WhatsApp can keep a single copy for each video shared by millions of different users (and the people share mostly popular videos, not personal videos), therefore the space consumed per user should be quite low.
WhatsApp doesn't have the feature to save videos to a cloud. As soon as you download a video sent to you, WhatsApp deletes it. 

You can have all your WhatsApp messages and media backup to Google drive, but that's not easily accessible unless you restore all messages from Google drive (usually done when switching phones or data loss.) 

My suggestion is to get an app that will backup your phots/videos. Like Google phots. 

Or you can move all videos to your SD card and then delete them from WhatsApp.