The local cache partition setting always takes precedence over the global cache partition value.
These commands set the server-wide partition number to 4, and the number of partitions for pubs_cache to 2:
sp_configure "global cache partition number", 4
sp_cacheconfig "pubs_cache", "cache_partition=2"
The local cache partition number takes precedence over the global cache partition number, so pubs_cache uses 2 partitions. All other configured caches have 4 partitions.
To remove the local setting for pubs_cache, and use the global value instead, use this command:
sp_cacheconfig "pubs_cache", "cache_partition=default"
To reset the global cache partition number to the default, use:
sp_configure "global cache partition number", 0, "default"