This is the Marble House, completed in 1892 for William Vanderbilt, the grandson of Commodore Cornelius Vanderbilt. It was designed by the architect Richard Morris Hunt, who was the first American architect to have studies at the Ecole des Beaux-Arts (from 1846 to 1855). At that time, It cost $11 million to build, equivalent to nearly $250 million today, and two thirds of the cost was for nearly 500,000 cubic feet of marble. I have read many times that it was inspired by the Petit Trianon at Versailles, but I do not see much resemblance between the two.