That gets us back to the question of whether it's necessary to back up data that's already in the cloud.
At this stage in the evolution of cloud storage, there's no definitive answer to the question of whether it's necessary to back up data that's already in the cloud.
If you've chosen your service provider well, the cloud is most likely going to be at least as safe as and probably more so than anything you devise yourself. Professional companies are in the business to earn money, and their reputation and success depends upon protecting your data.
Another thing to consider about your storage provider is what the fine print in the agreement you sign says about how readily available your data will be. If you need to access it only periodically, you'll probably be fine. Certainly if the data is something you could live without, even if you'd miss it, you can probably skip additional backup. It's highly unlikely that you'll lose your data.
But if you're very cautious, you might want to provide additional back up for any items of absolutely critical data whose loss would cause you severe problems in your business or personal life. You might want to provide your own additional redundancy for them. Back up those especially valuable items up somewhere other than on the cloud, and store them away from your home or office. Just for the peace of mind.