Can't find the reference but there were comments recently that President Trump made some reference to the White House but the remark implied usage or reference as white house (no capital letters)

the white house

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THE WHITE HOUSE

https://duckduckgo.com/?q=image+eisenhower+executive+office+building&t=opera&iax=images&ia=images

https://upload.wikimedia.org/wikipedia/commons/0/0e/Eisenhower_Executive_Office_Building_2021.jpg

Zoom in on the street sign!

18 December 2020 South Court Auditorium of the Eisenhower Executive Office Building (EOOB).

Listen as Vice President Pence begins his speech, and greets some of the principal officers and office holders present. Transcript of Pence opening remarks below followed by timestamp link to speech.

Begin transcript:

"Well, thank you all for being here today... to Acting Secretary of Defense Chris Miller, to the Secretary of the Air Force Barbara Barrett, to General Hyten, General Jay Raymond, General James Dickinson, General David Thompson and General David Allvin.

On behalf of The First Family... welcome to the White House,

And welcome to the first anniversary of that branch of our armed forces that will ensure for generations that America remains as dominant in space as we are on land, on sea and air.

Welcome to the first anniversary of the United States Space Force.

Many kind things have been said about your Vice President, but I have to tell you I am the second biggest champion of the Space Force in this administration.

So as we begin allow me to bring greetings and first anniversary congratulations from a champion of everyone that wears the uniform of the the United States and the founder of the United States Space Force.

I bring greetings and congratulations from the 45th President of the United States, President Donald Trump."

End transcript.

https://youtu.be/UfDTXnjMcgg?t=1263 (timestamp to start of Pence remarks)

What does Vice President Pence mean when he says, "On behalf of the First Family, welcome to the White House?"

Why does Vice President Pence first extend a welcome from The First Family to the White House and later extend greetings and congratulations from President Trump?

Does that make any sense at all?

https://upload.wikimedia.org/wikipedia/commons/0/0e/Eisenhower_Executive_Office_Building_2021.jpg

EEOB located near the West Wing of the White House, houses the Executive Offices of the President and Office of the Vice President. EEOB is connected to the West Wing of the White House by tunnel corridor.

Source for speech location listed in transcript (below) of VP Pence remarks:

https://trumpwhitehouse.archives.gov/search/?s=National+Space+Council