In many stories there are demons who ask Brahma for immortality boon and he refuses. But there are other stories where Shiva and Vishnu grant immortality boon. How can they grant this boon? What other gods have granted immortality?
In many stories there are demons who ask Brahma for immortality boon and he refuses.
There should not be any doubt, even Vishnu and Shiva refuses if the recipient is not worthy enough.
It doesn't mean that Brahma never granted boon of immortality to anyone or didn't have power to grant such boons. As per UTTARA KANDA of Valmiki Ramayana, Brahma granted the boon of immortality to Vibhishana:
Thy thoughts, O destroyer of enemies, do not originate in sin, I confer on the immortality. Having said this (to Vibhishana), he (Brahma) intended to grant boons unto Kumbhakarna.