[Jprogramming] solution to a challenge problem

[Howell, Leonard W. (MSFC-VP62)]

I'm at a Mathematica workshop and the class was given this challenge problem:
 
Find integers a,b,c,d such that a^3 + b^3 + c^3 +d^3 =31
 
and in general, write a program to give the solutions to a^3 + b^3 + c^3 +d^3 =k, k=1,..., 350.
 
Of course, some will be the empty set.
 
Anyone have an approach for this problem?