Megan has 1200 sugar cubes?

As a rule a large cube is constructed by n small cubes high by n small cubes wide by n small cubes deep.

So if it is wanted to use 1200 small sugar cubes to build a bigger one, that will mean that : n x n x n = 1200 ; n³ = 1200 ; n = ∛1200 = 10, 627 ∴ n = 10, 627That result shows up that n is not a integer number, so a big perfect cube can not be built if we wish to use 1200 small cubes.

So, the wanted bigger cube will be get jusing just 1000 small cubes that will be formed by 10 cubes high by 10 cubes wide by 10 cubes deep.

So the right answer is the girl just will be able to build a bigger cube formed by 1000 small cubes from those 1200 total cubes.

Your welcome.