First off, have you considered how heavy this tank is going to be when full of water? The total weight of the water contained in a 31.5"x25.6"x25.6" tank is 744 lbs.
The total force on each wall is a function of pressure, depth, and wall area. Integrating all of that over the surface gives a total outward force of 459 lbs on each side.
You'll need to know the ultimate tensile strength of the particular type of glass you're using. I'd recommend looking for tempered glass, which will have a higher strength.
For a rectangular plate of toughened glass supported along all edges (meaning, including a top brace), I found the following generalized formula for a maximum uniform pressure loading (PDF link):
Pmax (psi) = 84000*t^2/Af
where t is the glass thickness in inches
A is the area in square inches
f is the safety factor (10 in this case)
(I'm pretty sure it's supposed to be the thickness parameter that's squared, not the constant as it was written in the source material. Also take this number with a grain of salt, since the source material has an apparent typo in the equation. Wikipedia has a much more in depth derivation here.)
Using the parameters you specified along with a safety factor of 10, the max allowable uniform pressure loading is 2.2457 PSI. So your choice of materials should be OK for the non-uniform loading with a max value of 1.138 PSI. Note that this is for a piece of glass that is fixed along all edges, so that would mean you've got it secured to a brace along EVERY jointed vertex to counter the bending moments at the edges of the plates.
Also consider the strength of your adhesive if you're set on going frameless. It's going to be under a max stress of about 8.04 lbs/linear inch, in both shear and normal stress if you're doing the corners as butt joints.