A painter is going to paint a room shaped like a cube. With square walls that are 20 ft on each side. A gallon of paint can be used to cover 400 square feet. How many gallons of paint should the painter buy if he is going to paint the four walls of the room

Each wall of the room has an area of 20 ft x 20 ft = <<20*20=400>>400 square feet.

Therefore, the total area of the four walls is 400 square feet x 4 = <<400*4=1600>>1600 square feet.
Therefore, the painter should buy 1600 square feet / 400 square feet/gallon = <<1600/400=4>>4 gallons of paint. Answer: \boxed{4}.