How to secure delete inside a virtual machine?

Here is a tricky one: Can you securely delete a file from a VM?

I'm sure the answer is dependent on a million different variables, and I'm sure the answer is something like "not really" but I want to hear what the experts think and why.

If secure delete is not possible via conventional methods like shred, is it possible via unconventional methods?

If secure delete is simply not possible (or beyond the capability to assert) then what is the implication for "the cloud"? Is "the cloud" simply not viable for security? Or does it mean we must use full disk encryption at all times in "the cloud"?