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Part a :The cubes displaying a solitary black face are the ones situated within the cube's interior rather than along its edges. Removing the outermost cubes on each face reveals a $3$ by $3$ array of cubes, each featuring paint on just one side. Consequently, there are 9 such cubes per face, each exclusively black on one side, resulting in a grand total of $9\times 6=\boxed{54}$ of the smaller cubes exhibiting a single black face.

Part b: The "outer shell" of your cube has been painted, but if you take it away, it reveals a $3$ by $3$ cube inside, then you can multiply to get 27