Let 'A' represent the area of the smaller cube then the area of the larger cube is 6A.

The ratio of the areas of the two cubes is:

6A : A = 6:1

If the side of the cube is x, then the area is proportional to x² (the area of the cuber is 6x^2), and the volume is proportional to x³.

Also we can say that the volume is proportional to the area to the (3/2) power since x^2 to (3/2) power is x^3.

Now the ratio of the two volumes would be: 6^(3/2) : 1^(3/2) =  6^(3/2) : 1 = 6√6 : 1.