Linear separability in a 2×2×2 cube

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Essentially, linearly separable points are just those corners that can be cut off with just one slice as marked out by a hyperplane. Can someone please explain how many cases there are for a $2\times2\times2$ cube?

The number of linearly separable cases are more in a $2\times2\times2$ than a $1\times1\times1$ cube.

I'm not sure how to calculate the number of possible cases for a $2\times2\times2$ cube. The case below is just one of many, and I would very much appreciate help with this.

Thank you.

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Bottom left is an example of a linearly separable case. Bottom right is not linearly separable.