Can I Install a 60 AMP Breaker and Outlet with 220 – 240 Volts 63 Amp in My Home?

I am not an electrician. I am a sysadmin. I am trying to hook up a power-hungry blade server in my home and I am woefully ignorant on the subject. I have researched enough to ask a questions that I believe may be understandable to professionals. I am hoping to get enough information so that I can contact a professional to do the work and waste as little of his or her time as possible.

Here is a picture of my box:

I’ve read that these things can handle breakers totaling double the amperage of the main fuse. As I understand it, that means that this box can have 200A worth of circuits. By my count this box is at 135. Can this box handle a 60 Amp Breaker?

Furthermore, even if this box can take such a circuit. That’s kind of the beginning of the road. According to this document: http://media.community.dell.com/en/dtc/attach/white_paper_c07-443792.pdf

My server should be powered by a 48 Amp Single-Phase (as three-phase is out of the question, according to my wife) Power Distribution Unit, and that the recommended mating receptacle for such a PDU is Hubbell 363R6W 60 Amp.

As far as I’ve been able to gather, this is the outlet to which they are referring:

https://www.stayonline.com/detail.aspx?id=11661&gclid=CjwKCAiAk4XUBRB5EiwAHBLUMfHDSBq6p2fD5vwVQ9Vvg2bPGYg-EmMhikH0OYumQXcFSWXHSBtDvhoCnPgQAvD_BwE

So, I guess what I’m wondering is, am I crazy? Is this even possible to do for $1000 or less?

Please also consider the alternate solution.

Alternately, I could have 2 x 30 Amp breakers with the more common NEMA L6‐30R plugs.

I don’t really want two special outlets. I’d prefer to have one. But if running a 60 AMP circuit with the unusual Hubbell 363R6W is preposterous, I suppose that would be the only viable solution.

Thanks again for your consideration. Your input is valued, even if you are just laughing at me for being inexperienced.