Futurology

First of all I want to make sure we have the same definition of radiator in this context. Pedantic, but important to avoid misunderstandings:

Radiator, noun. It is NOT similar in shape to any heater or something with cooling fins you have in your household. My pet peve is that the ovens that are commonly referred to as radiators do not depend on radiation at all to function, but instead uses convection. For convection to work, you will need a lot of surface area to exchange heat with the surroundings. And for your surroundings to dissipate this heat, they need to have a gas or liquid (yes there are exceptions where solids also work, but that's besides the point). Without an atmosphere, there's simply nothing around that can dissipate the heat.

However, there is something in the context of space travel that actually is a radiator, simply because it depends on radiation to dissipate heat instead of convection. The radiation in question is infrared radiation. Anything with a temperature emits IR. The higher the temp, the more powerful the IR. Heat is conducted to the radiator panels which in turn radiates said heat away in the form of IR, which in turn cools down the coolant or heat pipe or whichever method of heat transport is used.

This is a method that is commonly used for thermal management in space. If you look up pictures of ISS, you can see them as these vaguely solar panel shaped white-ish grey-ish panels that extend out from the station itself, 90 degrees off set from the station itself. And those 90 degrees are a clue: They need to be angled 90 degrees relative to the sun, otherwise they'd pick up more heat than they dissipate. So at 90 degrees offset you effectively have two surfaces that can radiate the heat away, this results in the need for smaller radiators than solar panels.

Side note: If I'm not mistaken, the large solar arrays also radiate heat away from the sun, but it's not as efficient.

Now, the main problem with your suggestion. While it is possible to use radiator panels to cool the servers, you can't really sanwhich them due to the 90 degree offset. And you also need to keep in mind that ISS is built to use relatively little power, and thermal management was part of the design process from the start. With a datacenter you're going to use massive amounts of solar panels to power the thing. And each watt of electricity used is effectively turned into heat which results in the need for a massive amount of radiators. A rack with servers heat up FAST if not properly managed from a thermal perspective. I'm pretty sure that to power and cool one full-size 19" rack you're going to need so many panels (power and cooling) that you're going to have to build a huge structure on which you can mount it all.