The image above shows a construction of fractals by joining smaller and smaller cubes to each face of one single cube.
- We start with a cube of side length 3.
- In the second figure, the 6 new cubes are formed with a side length of of its previous cube.
- Then from the third figure and so on, the new cubes can only be formed on the 5 faces of the previous cubes with side length of its previous cube.
This recursion continues indefinitely.
If is the total surface area of the figure (from the left), what is the value of ?