If light has no mass, then why can't light escape the gravity of a black hole?

The speed of light isn't always the same. When people say that the speed of light is constant, they mean that if the density of the medium through which the light travels doesn't change, then the speed at which the light travels won't either. Gravity affects density, so, yes, the speed of light is affected by gravity.

The figure usually quoted, though, for the speed of light is based on the speed light travels at in a vacuum. In a vacuum, the density is constant, at zero, meaning there's no resistance. The speed of light in a vacuum is constant.

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