What is the number of small cubes which have exactly three faces painted?

Initial total number of cubes = 343,
Number of cubes removed = 27
Smaller 27 cubes painted blue
Exposed faces of original big cube (3 faces with 9 cube on each face i.e total 27 cubes) painted with black
Since 7 corner (Vertices) of bigger cube is untouched hence they are painted with three faces.
Now consider the corner from where we have removed 3 x 3 x 3 cubes,
After removed 3 new corners of the bigger cube will be generated that will be painted with 3 faces and 8 corners from smaller cube of 3 x 3 x 3 painted with 3 faces.
So the such total number of such cubes is 7 + 3 + 8 = 18.