back-up to iCloud instead of external hard drive ?

only for an IOS device - this my help you understand the iCloud services that are available - iCloud Deconstructed

this explains IOS backup - iCloud: Back up your iOS device to iCloud - Apple Support

How to back up your iPhone, iPad, and iPod touch - Apple Support

LN

Since your post is in the "iCloud on my iOS devices" forum, I concluded you are asking about backing up an iOS device.

If you are asking about backing up a Mac, the answer is no. You can however sync data from a Mac to iCloud Drive.

Syncing is not the same as a backup. For one thing, any change you make, including for example an accidental deletion, is automatically synced to iCloud. But it does allow you to have some or all of your data in a second location.

You can backup to iCloud or to a computer via iTunes.

See the following for instructions:

iCloud: Back up your iOS devices to iCloud

and

How to back up your iPhone, iPad, and iPod touch - Apple Support