I make a 6 x 6 x 6 solid cube out of 216 individual unit cubes of side 1cm.

What is the surface area of this cube?

I now make a new solid from the 6 x 6 x 6 cube by removing 16 cubes, one by one, each time taking the cube from the outside of whatever solid I currently have.

Clearly the volume of my new solid is 200 cm³, but what is the minimum possible surface area it could have? Explain how you can be sure of your answer.