WASHINGTON » After delivering an address in Denver in July, Vice President Joe Biden was shaking hands with members of the audience when someone yelled out to him.

“Maj. Beau Biden. Bronze Star, sir. Served with him in Iraq,” the man said, Biden recalled Thursday during an interview with Stephen Colbert.

“I was doing great,” Biden continued. But then, “I lost it. You can’t do that.”

It’s been more than three months since Biden lost Beau, his eldest son, to brain cancer, forcing the vice president to contend with personal tragedy in the public eye for the second time in his life. During that time he’s invoked his son’s name on occasion. And he’s acknowledged the difficulty of his family’s grief in repeated explanations about why he is not yet ready to decide whether he’ll run for president.

But Biden had said little publicly in detail about his searing loss until Thursday’s interview with Colbert, the new host of CBS’ “Late Show,” who urged Biden to tell a story about his son.

In his final months, with the family aware his condition was terminal, Biden recalled how concerned his ailing son was for him and marveled at how his son never complained while sick.

“I never once, my word as a Biden, never ever heard my child complain,” he said. “I was a hell of a success. My son was better than me. He was better than me in every way.”

When CBS announced Biden would appear on the show, many immediately suspected Biden might use the moment to announce once and for all his decision about 2016. Sure enough, Colbert at one point said he had to address the “elephant in the room,” or perhaps more appropriately “a donkey,” and asked, “Do you have anything to tell us?”

“Yes,” Biden said, suspense building. “I think you should run for president again and I’ll be your vice president.”

It was one of only a handful of lighter moments in an otherwise weighty sit-down. Colbert quickly followed up to ask whether Biden was emotionally prepared to run.

“I don’t think any man or woman should run for president unless, No. 1, they know exactly why they would want to be president, and 2, they can look at folks out there and say I promise you have my whole heart, my whole soul, my energy, and my passion,” Biden said. “And, and, I’d be lying if I said that i knew I was there. I’m being completely honest. Nobody has a right in my view to seek that office unless they are willing to give it 110 percent of who they are.”

Colbert said the nation had been inspired at the way Biden has handled tragedies. Biden’s wife and 1-year-old daughter were killed in a car accident weeks after he was first elected to the Senate in 1972.

Biden said the attention was “a little embarrassing” for him.

“So many people who have losses as severe or maybe worse than mine and don’t have the support I have,” he said. “I feel self-conscious. The loss is serious and it’s consequential, but there are so many other people going through this.”

He said that his faith helped sustain him, and he said he felt he would be letting his family down, including Beau, if he let his grief overtake him — that he needed to “just get up.”

“I marvel at the ability of people who absorb hurt and just get back up,” Biden said — including Colbert among them. The comedian’s father and two brothers died in an airplane crash when he was a boy.

“You’re one of them, old buddy. Losing your dad when you’re a kid. It’s like asking what made your mother do it every day?” he said.

“She had to take care of me,” Colbert said.

“I imagine,” Biden answered, “that would be a hell of a job.”