smc

The volume of each cube follows the pattern of $n^3$, for $n$ is between $1$ and $7$. We see that the total surface area can be comprised of three parts: the sides of the cubes, the tops of the cubes, and the bottom of the $7\times 7\times 7$ cube (which is just $7\times 7=49$). The sides areas can be measured as the sum $4{\sum }_{n=1}^7{n}^2$, giving us $560$. Structurally, if we examine the tower from the top, we see that it really just forms a $7\times 7$ square of area $49$. Therefore, we can say that the total surface area is $560+49+49=\boxed{658}$. Alternatively, for the area of the tops, we could have found the sum ${\sum }_{n=2}^7((n{)}^2-(n-1{)}^2)$, giving us $49$ as well. Note: The area on top and bottom are 49 because the largest area is 49, and the other cubes are "inscribed" in it.