question of the week

The great mathematician Romero, no doubt inspired by the Pythagorean equation C2 = A2 + B2,
examined the equation X3 = A3  + B3  + C3  and developed several interesting identities based on it.
For intance, 6 is the smallest positive integer such that its cube is the sum of 3 other cubes of 
integers: 63 = 53 + 43 + 33. It is interesting to note that most numbers have this property.

It is your task to find the number of integers, x, that have the property, that it can be written 
as the sum of 3 positive integral cubes, in the range between two given integers a and b, including 
the limits a and b.
Data.txt (you will need to create it) contains 10 lines: 5 pairs on lines, each 
containing a positive integer. The first integer of the pair is a, the lower limit of the range and 
the second integer is b, the upper limit of the pair. All input data are between 1 and 999.

Sample Input:

1 34
56 77
100 200S
150 600
900 999

Sample Output:

There are 12 numbers between 1 and 34 whose cubes are Romero Cubes
There are 13 numbers between 56 and 77 whose cubes are Romero Cubes
There are 73 numbers between 100 and 200 whose cubes are Romero Cubes
There are 367 numbers between 150 and 600 whose cubes are Romero Cubes
There are 90 numbers between 900 and 999 whose cubes are Romero Cubes