But, more importantly, how much Reddit costs to run, at their current scale, is immaterial. Reddit has raised $50 million in VC money and is valued at $500 million, that means that half a billion is the mark they are expected to meet/exceed in lifetime revenue, independent on what their costs are. For better or worse, for-profit startups have very different incentives than non-corporate internet communities. This allows Reddit to not be 4chan (wider audience, some level of control on trolling and harassment, etc), but at the same time, it can't be 4chan (including running on a ramen-for-one-and-electricity-bill budget if need to be)
Normally I'd suggest they start another business doing some honest work (i.e. not ad revenue). Say, a hosting service, since they have experience with that already. Reddit then could become a marketing expense for them - something they'd run for the sole ability to say "Yes, we're the ones who're running the Front Page of the Internet! As you can see, we have some experience!".
But, as you said, they took VC money. It changes the picture significantly. I'm not sure they can be helped.
In every get-rich-quick scheme there's a catch. In startups, the catch is that if you care about your product then taking VC money is a difficult decision because it means surrendering your business to the whims of people who absolutely don't care about your product.
Craigslist wiped the entire classified ad industry and much of the newspaper industry off the face of the earth merely by being the low-cost provider. Ad-supported businesses should be afraid. Very afraid.
As for Reddit, the VCs may have to take a haircut.
Is the content mostly text or does it have a lot of images/videos/sound files? If the former, it's a lot cheaper to run than the latter (hence why a lot of big community sites are so 'vanilla').
What's the audience/topic? Some fields are easier to monetise than others. People in tech are more likely to use Adblockers, but they're also more likely to try out new methods of monetisation (like say, a Patreon type system or something involving Bitcoin).
How much do you know about running a server? Much cheaper to run a big site on an unmanaged service than a managed one.
How many people post vs how many people read. More posting in less time = more server resources and more service costs.
What script do you use? Something lightweight and lacking in a lot of features is going to hold up for longer on a shared server than something like XenForo or IPB or VBulletin.
So it can be really cheap if you're after a simple forum with an audience that doesn't block ads and might be willing to spend a lot on subscriptions or donations. It can be really expensive if you're offering a live video chat microblogging/livestreaming service.
I've seen large forums with hundreds of thousands of posts on $5 a month hosting, and sites with about 50 users needing a dedicated server.