If I understand your question well, you want something like how this is done in Dropbox:

1. use the "Copy link" button next to a file on your Dropbox to copy a shared link https://www.dropbox.com/s/wgtgyulkk17vh6p/HRCoronalImager.jpg?dl=0 to that file. If you put this URL in your webpage, clicking it would bring you to the Dropbox website. Therefor you have to

2. change the ?dl=0 to ?raw=1, that is https://www.dropbox.com/s/wgtgyulkk17vh6p/HRCoronalImager.jpg?raw=1. That is a link that you could use in an <IMG SRC=> tag to embed an image in your webpage.

3. alternatively, change the www.dropbox.com to dl.dropboxusercontent.com, that is https://dl.dropboxusercontent.com/s/wgtgyulkk17vh6p/HRCoronalImager.jpg?dl=0. Possibly this works only for older Dropbox accounts.

Note 1

This feature is documented on Dropbox's help pages, but both alternatives are advised against elsewhere. Your Dropbox account is not intented to be used as a free webserver. Just like your Mega account (see the answer)

Note 2

I am currently testing this feature. The example links used will remain valid for a limited time only.

Answer

Alas, the answer is no, as far as I know mega.nz does not have such an option. I deduce it from the fact that mega.nz documents such a feature, but limited to some video file types and by using their own player only. See https://mega.nz/help/client/webclient/cloud-drive#can-i-embed-video-files-5c2970bbf1b709c30b8b457a

If you are still interested, this is how it goes. mega.nz allows to embed a player for your mp4 and webm videos on your mega.nz drive. Files of these types get an extra option under their ... menu, titled embed code. It produces code for an HTML IFRAME, like this:

<iframe width="640" height="360" frameborder="0"
 src="https://mega.nz/embed/lJhgzSRA#KYdcdw2pMJ-KSdoX_3Ayvec6Y8PVpuYfcyz46fpQ7X-M!1a1m"
 allowfullscreen allow="autoplay;"></iframe>