Can I Install a 60 AMP Breaker and Outlet with 220 - 240 Volts 63 Amp in My Home?
Since your 100 amp, 240 volt service consists of 100 amp, 120 volt branches, you can have 100 amps of load on each of the two branches. Note that the AC has two 120 volt breakers with the handles connected together. That uses both of the 120 volt branches to make a 30 amp, 240 volt breaker. As shown the box has breakers totaling 75 amps on one branch and 80 amps on the other. If you add a 60 amp, 240 volt breaker you will have 135 amps on one side and 140 amps on the other.

You can have breaker capacity in excess of the main circuit breaker rating based on the assumption that many of the load devices will only be used for short intervals of time during a day. However if the server uses 48 amps all of the time, it would not be difficult to imagine a day when the AC is running a lot, the refrigerator is cycling on occasionally, you stick something in the microwave and your wife is vacuuming.

It may not be out of the question, but it is somewhat doubtful. The service is already nut up to today's code. Today, a residence should have two 20 amp circuits dedicated to kitchen counter outlets and one 20 amp circuit dedicated to bathroom outlets. A microwave and garbage disposer often have their own circuits.

The box itself is likely capable of handling 200 amps at 240 volts, but you may have service entry wiring only rated for 100 amps. An electrician may come and quote a price at no charge. You can not get a good answer without that, but there is likely a way to get it done. Note that 48 amps at 240 volts is a lot of power. That is like having the oven and all the burners going at one time in an electric stove.

You don't need the Hubbell 363R6W. Use a standard electric range outlet.