Number of Active Physical Processors

% grep physical.id /proc/cpuinfo | sort -u | wc -l
8

Number of cores per CPU

% grep cpu.cores /proc/cpuinfo | sort -u
cpu cores       : 26

Therefore the total number of cores is
8×26 = 208 cores

Number of Logical Processors

The number of cores seen by the Linux. Since the Server has switched on Hyperthreading

% grep processor /proc/cpuinfo | wc -l
416

References:

1. How to find the number of physical cpus, cpu cores, and logical cpus