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- Hypothetical situation: An algebra teacher was looking for examples of how the cubes of two integers might add to be the cube of a 3rd integer. Can you help the algebra teacher?

This post is meant to be a fun one. It is at the beginner level, because I think most people at the intermediate level would know what the solution is, but they might also find it entertaining as well. ## \\ ## A hypothetical situation: An algebra teacher observed that ## 3^2+4^2=5^2 ## and ## 5^2+12^2=13^2 ## and quite a number of others. The teacher wanted to give the class a little practice with some 3rd power arithmetic, and was looking for some integer examples where ##a^3+b^3=c^3 ##. Can you help the algebra teacher find a couple?