And even if it worked (and it would take a LOT of nukes to work) ... well, congrats: now Mars has an atmosphere -- a highly radioactive atmosphere.
Thanks to Mars's lack of a magnetic field, high radiation levels are already a concern. Adding even more radiation into the mix really isn't going to help any of your terraforming goals.
Data centers on floating barges (or submerged just below the surface) makes so much more sense.