You've heard statistics that say it takes light around 7 - 8 minutes to travel from the Sun to the Earth. That's nothing compared to the time it takes light to travel from the inside of the sun to the outer edge.
The reason for this is that the Sun is actually opaque at the center. Light doesn't bleed through that easily, and in fact, NASA compares it to 'slightly better than light travelling through a rock.' What happens is light comes out and goes a short distance, then is absorbed and re-emitted. When it gets re-emitted, it goes off in a random direction. This randomness makes it so that it takes light thousands of years before it reaches the outside, and finally Earth.