Answer
odd.
Work Step by Step
Step 1. Replace $x$ with $-x$, we have $f(-x)=-(-x)^3+2(-x)=x^3-2x\ne f(x)$, thus it is not even.
Step 2. Replace $x$ with $-x$, we have $f(-x)=-(-x)^3+2(-x)=x^3-2x=-f(x)$, thus it is odd.
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