Only twelve fighters appear
The rules describe aeras for spells in squares, not in cubes. They always talk about an area (2 dimensions), not a volume (3 dimensions).
The description of a sphere for example says:
A sphere-shaped spell expands from its point of origin to fill a spherical area.
Technically, it would need to say the spell fills a spherical volume, but since the majority of combat happens on the ground and a two-dimensional battle grid, to speed up and simplify play, the rules assume you only care about two dimensions.
You can see the same attitude in how distances are measured:
When measuring distance, the first diagonal counts as 1 square, the second counts as 2 squares, the third counts as 1, the fourth as 2, and so on.
This does only approximate the actual distances, it is a simplification to speed up play.
But what about fireball?
Now, while they say that, it is common practice to account for the areas of spells like fireball in three dimensions, and also affect creaturs that fly above the ground if they are low enough.
You could argue the same treatment should apply to these illusionary warriors. Especially because these warriors are described as ghostly and incorporeal, and incorporeal creatures such as ghosts often can fly.
A technical argument against this could be that a typical warrior would be larger than 5 feet in height, and since creatures in combat need space and cannot overlap, you at the very least could only create half of the number of warriors ... or you would need to create dwarf-sized warriors.
A gameplay argument against this is that this quickly gets too complicated to support flow during play. You end up bogged down calculating volumes, instead of playing out an exiting battle. (See also this in depth Q&A of how to handle 3D distance in 3.5e, the mere length of which gives you a good idea of what you are getting yourself into.)
All that said, if both you and your DM think it should work, and you should be able to summon a ball full of dwarf-sized spectral swordfighters, go and have fun with it.