Who is the only United States president who never lived in the White House?

George Washington

Actually, there were several Presidents of the United States who never lived in the White House. The United States, as a nation, started its existence when Maryland signed the Articles of Confederation.
"Maryland on February 2nd 1781 final ratifies the Articles of Confederation. On March 1, Maryland’s ratification is presented to the Continental Congress. With all the thirteen States present the Continental Congress declares the Articles ratified forming the perpetual Union of the United States of America." - US Presidency.com

The following men held the office of "President of the United States, in Congress Assembled":

Samuel Huntington (March 1, 1781 - July 6, 1781)
Thomas McKean (July 10, 1781 to November 4, 1781)
John Hanson (November 5, 1781 to November 4, 1782)
Elias Boudinot (November 4, 1782 to November 3, 1783)
Thomas Mifflin (November 3, 1783 to June 3, 1784)
Richard Henry Lee (November 30, 1784 to November 23, 1785)
John Hancock (November 23, 1785 to June 6, 1786)
Nathaniel Gorham (June 6, 1786 to November 13, 1786)
Arthur St. Clair (February 2, 1787 to October 29, 1787)
Cyrus Griffin (January 22, 1788 to March 4, 1789)
On March 4, 1789, The United States Congress held its first session, under the authority of the US Constitution, and ending Griffin's term. George Washingtion was inaugurated April 30, 1789 as the first President of the United States under the Constitution.

(The John Hanson Museum even boasts of a letter in its possession, congratulaing Hanson on becoming President. The letter is signed by Gen. George Washington.)

Prior to the signing of Maryland, the title was "President of the Continental Congress." Once the Articles were ratified, the Congress changed the title on March 1,1781 the title of the office changed to President of the United States in Congress Assembled. Samuel Huntington, the President of the Continental Congress, stayed as President, and thus became the first President of the United States, as named and elected by the only goverment of the United States at that time.

(In earlier posts on AP, I stated that Hanson was the first President of the US. More research showed that I was wrong. Hanson was the first to not use "In Congress Assembled" when signing documents.)

"All we want are the facts, ma'am." - Sgt. Joe Friday

Judy, I assumed that your question reflected the Presidents of record; I Stand by that answer.

Dorian is historically correct, although I don't think that was the intent or spirit of the question.