This perennial problem has led to many articles in the Gazette (listed by Sullivan in the June 1987 edition) many of them geometric or combinatorial in nature. If we look at some older algebra texts, published before the 1960s say, we see that the method of differences is one of the standard methods for dealing with the problem. With the current interest in discrete mathematics this method merits re-examination. A feature of the method is its effectiveness in finding the solution to the problem for all powers and it is not limited to the sums of squares and cubes. In this article we hope to show that it can be treated more transparently using the calculus of finite differences.