How long would it take for a beam of light to travel around the earth in an ideal fiber-optic cable?

The speed of light in glass is less than c by a factor of about 0.7. It depends upon the type of glass material used. Being "ideal" means there are no losses, but not that the speed of light is c.

Divide the circumference of the Earth (40.1*10^6 m) by 0.7 c (about 2.1*10^8 m/s) for an approximate answer.