CBS /
Cook and Colbert discussed a variety of subjects, but only one elicited a lengthy, heartfelt response from Cook.
Colbert asked Cook about the CEO's letter in October 2014 in which he publicly announced that he was gay.
"Was coming out an upgrade, or a feature that hadn't been turned on?" Colbert jokingly asked.
After a bout of laughter, Cook said he felt it was time to use his position as a means to help others who may not feel emboldened to be open about their identity. "Life's most persistent question is, 'What are you doing for others?'" Cook said. "I feel a tremendous responsibility to do it."
In terms of the feeling of coming out, Cook took a characteristically Apple-centric approach to his answer: "It's like discovering something on your iPhone that it's always done, but you didn't quite know it."
Cook echoed many sentiments previously discussed in his open letter from October 2014. He wrote in Bloomberg Businessweek at the time, "Being gay has given me a deeper understanding of what it means to be in the minority and provided a window into the challenges that people in other minority groups deal with every day."
CBS /
Much of the interview otherwise focused on the new iPhone 6S and its two big selling points: a new form of input called "3D Touch" and a GIF-like function called "Live Photos." Cook quickly moved past Colbert's question about Apple working on self-driving cars - a follow-up to the assertion by Uber's Kalanick last week that Apple was indeed working on such a project - saying only that Apple considered many projects.
The interview also touched on Apple's struggle with working conditions in the Chinese factories where its products are made, though Cook lacked passion in his answer. Instead, he described Apple's efforts in its factories as, comparatively, a success.
You can watch the portion of the interview in which Cook talks about coming out here: