Since you are new and do not know a lot of things, you have to deal with the situation carefully.
My suggestion would be to bring up the issue with your immediate reporting manager to gather enough data. Do not mention your colleague at all. In fact, pretend that you do not even know of his doings. For example, you could talk to your manager (let's call him John) something like: "Hey John, I have been working here for a while now, and I was curious about a few things. You see, we have all these spare machines, and they are not doing the project computations during off-hours. I wonder if we could use those extra resources to complete our project sooner (etc.)"
Most likely, someone already thought of that before, and decided it cannot be done. Maybe you know it yourself that the spare resources cannot be used, but as a first step, you convince your manager that you want to add value to the project as opposed to looking for a way to put them to personal use.
If your manager explains why it cannot be done, then you could continue with, "In that case, I wonder if it would be okay for someone to use the them for their personal use." You should not jump to this step by skipping the first step mentioned above. Do not mention the specific purpose that your colleague is using it for. That would make your manager curious, and you are not ready to reveal enough yet.
Let's say he says this is allowed. Then you ask a specific question, "Well, I wonder if that is really okay. I mean, what if someone uses them in the off-hours to make money? Would that violate the contract or cause some other trouble?"
Now clearly, if he says, using company's spare resources to make money is not allowed, you just tell him what you observed without sounding like you are selling out your colleague. For example, "John, actually the reason I asked you this is I have seen Bill do this a few times. Maybe he is not aware of how the contract is interpreted." You want to sound like you are trying to help your colleague out of a potential legal problem in future (which you are doing, by the way).
On the other hand, if he says this is allowed, you could just mention what your colleague was doing, again without sounding like a complaint. "John, Bill showed me this interesting thing the other day ..."
When I started writing, I did not think this would be so long. Sorry about that but the key points to handling this from my perspective are:
- Since you do not know how things work, gather required data step by step. The above hypothetical conversation might span several meetings.
- At all points, and even if you have to escalate, give your colleague the benefit of doubt. You are not trying to cause him trouble, you want to prevent him from getting into trouble.