How long can I stare at the sun before it does damage to my brain?

Technically, the retina of your eye is the only portion of the brain outside of the skull.

http://hubel.med.harvard.edu/book/b8.htm

You can damage your retina within only a few seconds.

That's brain damage. Period.

http://en.wikipedia.org/wiki/Sungazing

http://en.wikipedia.org/wiki/Solar_retinopathy

That can cause permanent vision loss, in fact, it is one of the most common causes of blindness.

Let me give you a heartfelt piece of advise: don't be an idiot.

the problem is to ur eyes not ur brain

"The practice of sungazing is dangerous. Looking directly at the sun for even brief periods of time may cause blindness or severe damage to the eye.[5] Solar retinopathy, damage to the eye’s retina due to solar radiation,[6] and blindness to varying degrees and persistence frequently result from sungazing during a solar eclipse.[2][7] Although vision loss due to this damage is generally reversible,[6] permanent damage and loss of vision have been reported.[8] Most eye care professionals advise patients to avoid looking directly at the sun.[9] Exposure to ultraviolet radiation, produced by the sun, is associated with damage to the eye, including pterygium[10] and cataracts."

First of all, you can't stare at the sun and this is not cancer, no matter how brain damaged you are.

Your brain will be fine.

Your eyes, however, will probably be damaged at least temporarily.

one day