I'm not entirely certain what the fluffiness of a cake is, but if I'm right in that it's air inside of the cake, then you can measure its density.

Step one: weigh the cake. First take a plate, and weigh it on a scale. Then, put the cake on the plate, and now weigh the cake and the plate together. Subtract the weight of the plate alone from of the cake plus plate together. This will get you the weight of the cake. Equation:

weight of cake = weight of cake and plate - weight of empty plate

Step two: calculate the volume of the cake. If the cake is square, then the volume is the length of the cake, times the width of the cake, times the height of the cake. If the cake is round, then the volume is one half of the diameter of the cake, squared, multiplied by pi, and then multiplied by the height of the cake. Pi is roughly 3.14 (it's not exact, but it's close enough for your purposes. So, equations:

square cake:
volume = length x width x height

circular cake:
volume = (diameter / 2) x (diameter / 2) x height x pi
pi = 3.14

Step three and finally: calculate the density of the cake. Divide the weight by the volume.

Density = weight / volume.

Now, this number isn't going to help you unless you have another cake to compare it to. You will need to repeat this procedure for each cake you need the density for, but once you have the densities, you can compare them.

A cake with a lower density, that is less weight of cake per unit volume, will be a fluffier cake.

Density would be a good start (mass/volume) . The "fluffier" a cake is, the less dense it will be.

I like your experiment! A fluffier cake will have more air in it than a heavy cake. So you can cut a piece of cake - a cube or a rectangular piece. Then measure its 3 dimensions - length, width, height. Then weigh it. From the dimensions, you can calculate the volume, in cubic inches or cubic centimeters. From the volume and the weight, you can calculate the density, in grams per cubic centimeter or ounces per cubic inch. You can compare the fluffiness of different cakes that way.

If I were doing it, I would use my postal scale, for weighing letters and packages. Or I would use my little letter scale that only weighs up to 3 ounces or a few grams. To use the letter scale, I would put the cake in a sandwich baggie and hang the cake in the sandwich baggie from the clip on the letter scale. Or, I would use my 'diet' scale. It weighs things from 1 ounce to 1 pound, and you put the thing to be weighed on the scale. If you put the cake in a baggie or something to weigh it, don't forget to subtract the weight of the thing you put the cake in.

Keep asking questions!