MySQL using 100% of CPU with 1500 active connections
You may have encountered a Von Neumann Bottleneck. 

CPU usage is expected to increase as the number of connections increases.  As the connections increase the number of active queries should also increase.  Each query will use some CPU.  Eventually, you will have enough queries to use all available CPU. 

There are some additional factors that while use more CPU as the number of concurrently running queries increase:


Time spent waiting for resource locks.  This may involve a lock spin which will consume additional CPU. 
Context switching when the O/S switches the currently running query.  This is a side effect of the multi-processing that allows you to run more than one query at a time.


Running a program like sar may provide more details on where the CPU is being used.