There are two possible ways to think about this problem.
You could consider the surface area looking at the shape from each direction.
The shape looks like one of the two shapes on the right from each of the six directions, so the surface area is $ 6 \times 3 \text{cm}^2 = 18\text{cm}^2$.
Alternatively, 3 of the cubes have 5 of their faces showing, whilst the cube in the corner has 3 of its faces showing.
This means a total of $3 \times 5 + 3 = 18$ faces are showing, so the total surface area is $18\text{cm}^2$.