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April was asked to determine whether $f(x)=x^3-1$ is even, odd, or neither. Here is her work:$\newline$Step $1$: Find expression for $f(-x)$$\newline$$f(-x)=(-x)^3-1 =-x^3-1$$\newline$Step $2$: Check if $f(-x)$ is equal to $f(x)$ or $-f(x)$$\newline$$-x^3-1$ is the same as $-f(x)=-x^3-1$.$\newline$Step $3$: Conclusion $f(-x)$ is equivalent to $-f(x)$, so $f$ is odd.$\newline$Is April's work correct? If not, what is the first step where April made a mistake?