ClassiCube

No, ClassiCube cannot connect to Premium Servers. Bukkit.org also doesn't have any servers.

I just learned about Bukkit last night, so am still learning about it. Bukkit, at least from what I can tell, does appear to have servers. They have a GUI version called bukkitgui and their regular version which runs from craftbukkit.jar java file that you have to create a .bat file with a command for starting it.

Only thing is, I'm still a bit confused about what Bukkit does if it is not a minecraft server. The way it looks is that it's a server with a bunch of plugins available. But there is no clear description on the website of what it actually does. I thought it was a minecraft server and I just was not able to get connected to it.

Oh, and as far as I can tell Bukkit is free / not premium.

Guess I'm a bit confused about it, though.

Bukkit is a free server software for paid minecraft. It is one of the best ones for premium. It is, however, not classicube compatible or for classicube at all. It isn't affiliated in any way to servers that run bukkit other than the fact that they do. BUT this only applies to paid minecraft.

Bukkit is not a Minecraft server, it is an API for the official Minecraft server released by Mojang. Bukkit is a set of tools that allows developers to attach plugins to the official Minecraft server. Therefore, in order to run, Bukkit requires the Minecraft server located here: https://minecraft.net/download (at the bottom). In order for servers to run plugins created with the Bukkit API, they much have a program called Craftbukkit.jar downloaded and setup in their server.

Bukkit is free, but can only be used with Premium Minecraft since it requires the official Minecraft server. There is a GUI for Bukkit, but again, that is simply a plugin that someone wrote using both the official server and the Bukkit API. Since ClassiCube is not Premium Minecraft, both the official Minecraft server and Bukkit/Craftbukkit will not be able to run with it.

I hope that helped to answer your question.

tl;dr: no