"It really struck me when I heard about the news of Cook's brother," Archuleta says in a statement. "I know they had been struggling with it for a while, so my heart really goes out to them. It's so admirable the way he's handling it though, and it's amazing to see him there as an example for millions of other people who have also been affected the same way he and his family have."
Continues the statement: "I'll be keeping him in my thoughts and prayers, and hope the Cook family stays strong."
David Cook's brother, Adam, died on Saturday after battling cancer for more than a decade. Cook, 26, revealed the sad news in front of a crowd Sunday during the Race for Hope, which benefited the National Brain Tumor Society and Accelerate Brain Cancer Cure.