The new shape will still have a face for each of the 6 faces of the original cube, plus three faces for each of the 8 cubes cut out, for a total of 30 faces.
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$$
6 \text{(regular faces)} + 3\times 8 \text{(cut faces on each vertex)} = 30
$$
The new shape will still have a face for each of the 6 faces of the original cube, plus three faces for each of the 8 cubes cut out, for a total of 30 faces.