nungate - I believe that the Irish-American architect of the White House has no direct links with Edinburgh architecture per se. County Kilkenny born James Hoban was apprentice to Cork born Thomas Ivory in Dublin before emigrating to the US.
Forgive the following ramble, but it includes direct and convoluted connections to Auld Reekie...
To facilitate construction of Hoban's White House, master stonemasons were sought throughout the US and Europe; at least eight were recruited in Edinburgh. These eight masons, being Freemasons, were founder members of the Federal Lodge No.1 in DC, with the first Lodge Master being architect James Hoban. No doubt the Lodge would have been visited by President George Washington who had been initiated to Masonry four decades earlier in the Fredericksburg Lodge, Virginia - this lodge received its Charter from the Grand Lodge of Scotland, Edinburgh.
[Ramble ends]
Basil Paterson College makes proud claim that it "was built by the same stone mason that constructed the White House in America!".
http://www.basilpater..._language_school.html