Colbert also asked Woodward what he thought about Trump and some of his top officials - including James Mattis and John Kelly, who were quoted in the book - disparaging the new book.
The author said that several Trump officials were "not telling the truth" now that excerpts from the book are out, and that is understandable because everyone wants to stay in job. I've found that the best books about the Trump era are not really about Trump at all. "Woodward would have performed rudimentary journalistic fact checking with those he was quoting, he would have had a more accurate book rather than just being a stenographer for Mr. Bannon's self-aggrandizing revisionist history".
The publisher of Bob Woodward's book Fear is expecting one of the biggest publishing success stories of the year, printing one million copies to keep up with reader demand. If I did I would not have been elected President.
Of course, deep background - in which Woodward doesn't name his interviewees but uses their information - has its pitfalls, as the author is again discovering.
Julie Chen steps away from CBS's 'The Talk' after Moonves fiasco
CBS will pay ousted chief Les Moonves $120 million if its ongoing investigation fails to find any evidence of sexual misconduct. The executive is one of the highest compensated in media, making $69 million a year ago , according to regulatory filings .
Fear is set to be released on September 11, and as of Tuesday morning was already the fifth best-selling book on Amazon for the year, just ahead of former FBI Director James Comey's A Higher Loyalty.
By the looks of it, Woodward has plenty of grave, highly specific details to offer readers about the threat posed by the Trump White House, not just to its staffers but to everyone living under its rule.
"Well, the book is already out", he said.
"The Woodward book is a scam", Trump said.
Mr Mattis also issued a statement, re-tweeted at least twice by Mr Trump, saying, "The contemptuous words about the president attributed to me in Woodward's book were never uttered by me or in my presence". "And I'm not sure how he's going to handle it". Also, Woodward steers clear of Trump's controversial decision to move the US embassy to Jerusalem, thanks in part to the efforts of his ardently pro-Israel son-in-law Jared Kushner.
Honestly, Colbert's first question, about how on Earth people still think it's a good idea to talk to Woodward, is probably one that a lot of people have.