  We make several improvements to methods for finding integer solutions to
$x^3+y^3+z^3=k$ for small values of $k$. We implemented these improvements on
Charity Engine's global compute grid of 500,000 volunteer PCs and found new
representations for several values of $k$, including $k=3$ and $k=42$. This
completes the search begun by Miller and Woollett in 1954 and resolves a
challenge posed by Mordell in 1953.
