A Bruno number is a special number named after German mathematician Ernst Bruno von Sohn-Rethel. It is a number that can be expressed as a sum of two cubes in two different ways. For example, the Bruno number 34 can be expressed as 1^3 + 5^3 = 26^3 + 8^3. The number 1 is not a Bruno number because it can only be expressed as 1^3 + 0^3.