On a diophantine equation of Cassels

fJWS. Cassels gave a solution to the problem of determining all instances of the sum of three consecutive cubes being a square. This amounts to finding all integer solutions to the Diophantine equation y(2) = 3x(x(2) + 2). We describe an alternative approach to solving not only this equation, but any equation of the type y(2) = nx(x(2) + 2), with n a natural number. Moreover, we provide an explicit upper bound for the number of solutions of such Diophantine equations. The method we present uses the ingenious work of Wilhelm Ljunggren, and a recent improvement by the authors.