Series, Powers, and Benches
This looks pretty good. A few changes I would make:
Performance
10^10, 20^20, and all higher powers will always end in 0000000000, which means they don't affect the sum. You should be able to get an approximately 10% performance improvement by not computing these powers. This would be easy to do in your loops case but would require a little syntactical cleverness in the streams way.
Magic Numbers
You have a magic number 9110846700L in your code. It's not immediately clear what this is, especially if you are unfamiliar with the UBench library. This should be refactored into a magic number constant, in this case. Further reading on this subject
Static methods
Even for a program as simple as this, I would always shy away from putting your business logic in static methods. Obviously, in this case it isn't a problem, but for an application could grow at all, you will quickly regret it. More further reading
Inconsistent method scope
One of your methods is private, the others are public. Again, this issue is not super relevant for such a short program, but allowing encapsulation to be broken starts to matter as soon a program reaches two classes.