If the Earth has over 80 times the mass of the moon, why does it only have about 6 times as much gravity?

According to this source, “The moon is ¼ the size of Earth, so the moon’s gravity is much less than the earth’s gravity, 83.3% (or 5/6) less to be exact.”

From what I understand about the sizes of 3-dimensional objects, the volume is the size, and the diameter of a sphere is only a single factor in determining its size.

According to my calculations, the Earth is about 50 times the size of the moon.

Also, I thought the gravitational force of an object was dependent on its mass, and not on one dimension of its size.

I.e., I’m not satisfied with the explanation I quoted.