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Take the Ramanujan identities with - 1 given by him, e.g., 135^3 + 138^3 = 172^3 - 1^3 , etc., and transpose the - 1 to the left:
172^3 = 135^3 + 138^3 + 1^3.
We have a method for finding a cube which is the sum of three other cubes (one of these being equal to 1). this is (I think) a new result obtained "from the shoulders of a giant".
Raúl A. Simón.