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The algebraic part of Wieferich's proof holds for all integers exceeding 2J billion. The fact that all smaller integers are sums of nine cubes was proved by use of Table I. To prove my theorem, I shall need also the new Tables II and I I I . Table I gives, for each positive integer N^ 40,000, the least number m such that N is a sum of m cubes. I t was computed by R. D. von SterneckJ by adding all cubes to

All integers except 23 and 239 are sums of eight cubes