​Eight cubes form the figure shown.

The surface area of this thing is just a 3 x 3 x 1 box surface area minus 2 faces because there are still squares in the hole.

Surface area 

= (3 x 3) x (3 x 3) x 2 + 3 x (3 x 3) x 4 - 2 x 3 x 3

= 252 square centimeters

Let's just count how many cube faces are exposed..

 

8 on the front, 8 on the back

3 on the left side, 3 on the right side

3 on the top, 3 on the bottom

4 in the middle

 

That is a total of 8 + 8 + 3 + 3 + 3 + 3 + 4 = 32 exposed cube faces.

Each cube face has an area of 3 cm * 3 cm = 9 cm²

So.. the total surface area of this shape = 32 * 9 = 288 cm²

 

It's a  3 x 3 x 1 box SA minus 2 faces PLUS 4 faces.