Answer:
Many people including have supposed that the white house was painted white in order to cover burn marks left by British troops in 1814.
I just finished a guided tour of the White House today, where it was explained that the exterior walls were constructed of sandstone quarried from Aquia Creek quarry in Stafford VA.
The presidential structure was painted white in 1798, (16 years before the White House was burned) in order to protect the sandstone from damage caused by water and winter freezes.
The name "White House" did not become official until Theodore Roosevelt issued an executive order in 1901, although there are many references to "the White House" that predate the war of 1812.