But [1] will the data be worth anything and [2] will you still exist when/if it is broken?
I suspect there's a not-insignificant number of people out there who are glad they didn't make the encryption on their old data very strong (and likewise, those who regret having used very strong encryption and lost the key.)
He can't, but we also lack a proof that any of encryption is at all computationally hard to decrypt, so to err on the side of caution you should assume it.
TL;DR Encrypting is still better than not encrypting
Normal delete operations on common file systems don't wipe the stored data with zeros or random data either. They just mark the space as unused and make the directory entries invisible. Any tool that can read the disks directly can see the data even after it's deleted (though it may have trouble constructing it back depending on fragmentation of the data before deletion and the reuse of the freed up space). There are "undelete" tools available for different file systems that can try to recover your data after deletion (some additional conditions apply).
For cloud based backup providers, I doubt if any of those would spend time and energy wiping your data areas clean just because you deleted the data or asked for it to be deleted (since storage is also shared across customers, wiping clean your data would have a negative impact on other customers' data access speed too). They would just let the OS do its job, which would be what's described above.
You can run free tools to wipe a magnetic hard drive with zeros, run multiple passes, etc. With SSDs, that's not reliable because of the additional abstractions used and presented by the controller to the OS.
