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John has yellow, green, and red cubes, each with side length c. Eight yellow cubes are glued together to make a larger cube. An even larger cube is made by gluing on green cubes until no yellow cubes can be seen. After that, John covers the green cubes with red ones so that green also cannot be seen, making an even larger cube. The minimum number of green and red cubes were used to cover previous colors. What is the volume of the final big red cube?

Answer :

stepet50
The area of a cube is a= 6c^2. The volume of a cube is v= a^3. 

yellow large cube area is 6(2c^2). Because when we place the 8 cubes (use 4 cubes to make a square than stack another 4 cube square) to form the large cube the edge (length) is doubled. 

Looking at the pic. the large red cube's length is now 6 times longer than c.
a =6(6c^2)  ---> a= 36c^2       v= (36c^2)^3 ----> v= 36^3c^6  
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