Colonial expansion is seen in almost all architecture in the United States, since we are a very young country and were entirely colonized by European countries. Evidence of colonial expansion to the U.S. is seen in the U.S. capitol building in Washington, D.C. The facade of the capitol building is almost identical to St. Peter's cathedral in London, England. Large dome structures with many columns and large porticos are seen in cathedrals throughout England, France, Italy and elsewhere. The dome and columns gives the Capitol building an impressive, stately appearance, emphasizing the power of government versus the power of the church in England, during the days where the Church of England was the main authority.
St. Peter's Cathedral, London, England
U.S. Capitol, Washington, D.C.
Perhaps the only example of truly American architecture that I can think of are skyscrapers. The first skyscraper of steel frame construction, the Home Insurance building in Chicago, was designed in 1885 by American architect William Le Baron Jenney. The idea of skyscrapers became appealing to the rest of the world, by taking up less ground space in more densely populated areas as well as being symbols of power by dominating the skyline...giant "wu-wus". A modern example of a skyscraper is the Gherkin Building in London's financial district. We can see how skyscrapers have evolved from square stone buildings to more fluid forms using lots of glass, "dematerializing" the structure.
Home Insurance Building, Chicago Illinois ca. 1885
Gherkin Building, London, England