Question 1199951
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The cube starts off with 6 faces.


Drill a hole all the way through and we introduce 4 more inner faces. These are the inner walls of the tunnel.


If another hole is drilled through all the way, then another 4 inner walls or faces emerge.


A third hole is drilled, but not all the way through. This introduces 4+1 = 5 faces.
The 4 are the walls of this hole, and the +1 at the end refers to the floor so to speak. Imagine that this hole is a crater that you can stand in.


Total = 6 + 4+4+4 + 1 = 19 faces


Answer: 19 
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