Ah, you missed the obvious: pumpkin!
This is biologically a fruit, actually, as is the zucchini.
Pumpkin loves same spices as carrot. Maybe even rum or butterscotch too.
Now, beetroot is a veg and colors cakes delectably; perhaps why it was originally added when going stingy on the cocoa.
How about parsnip next? Sweet and nutty, I think pistachios would complement it well in a recipe borrowed from zucchini bread.
more veg here:
http://www.deliciousmagazine.co.uk/articles/how-to-make-cakes-from-vegetables
p.s. if you haven't guessed Rabarber is rhubarb
There are lots of people who have a rather simplistic approach to nutrition and think that removing fat and calories makes you healthy. Then they go through recipes for things they want to eat, replace the sources of fat with something which doesn't have fat and doesn't make the result outright inedible, and declare their recipe a success. I think this is what happened here.
In a cake, eggs provide leavening, moisture, smoothness, own flavor, and enhancement of other flavors. Oil provides smoothness and enhancement of other flavors (and possibly its own flavor, if not netural). And while it is not water based, it keeps the moisture in the cake from evaporating, so it makes the cake less dry.
If you are a "simplistic nutritionist" without all this information, you can approximate some of the effects with soda. It will provide moisture, and it will also provide some leavening because it is fizzy. It will provide some flavor of its own too, but frankly, I find the rather chemical flavor of soda to be unpleasant. And it won't have any fat. In the eyes of the simplistic nutritionist, it has successfully replaced the oil and eggs while reducing fat and calories.
From the point of view of a baker, the cake will be a disaster, and won't even deserve the label cake. It will dry out quickly because it has no fat. It will have a bland flavor. Its texture will be terrible. They say "more chewy?" It will miss both the protein structure and the emulsifying agents provided by the eggs. It will be essentially an overwhelmingly sweet quickbread with no redeeming qualities. From a culinary point of view, it will be terrible.
Bottom line: under some assumptions, it is a good substitution. For me, these assumptions are so far from reality as to be useless. It is a terrible substitution.
Best Answer
Glucose is very expensive, unlike caster sugar (sucrose, also commonly called "table sugar") which does the job, and is much easier to work with. Glucose in the modern kitchen is only really used in meringues.