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The docs patch doesn't look quite right - Peter, did you mean to copy the "is_private" docs before modifying them?
As far as caching goes, perhaps we can just drop functools.lru_cache into the relevant property implementations?
 @property
 @lru_cache()
 def is_global(self):
 """Test if this address is allocated for public networks."""
(also in copying that example method header, I noticed the docstring for the IPv4 is_global currently still says "private" instead of "public")