Unlike gravity, which incidentally happens to produce surface-area-minimizing shapes in 3D under the L2 norm, surface tension actually does produce surface-area-minimizing shapes when minimizing energy, and that holds regardless of the space in which it is operating.
So, "what is the equilibrium, minimum-energy shape of a small liquid drop in the cubiverse?" turns out to be equivalent to "what shape has the minimum surface area for a given volume?"
Well, in our universe, the answer is "a sphere", and in the absence of any obviously better starting point, we might as well go ahead and ask what the geometric equivalent of a sphere is in the cubiverse, and see if we can do any better by perturbing that solution.
The cubiverse-geometry equivalent of a circle is a square, and the equivalent of a sphere is a(n axis-aligned) cube. Now, what happens if you try to shave off the corners of a square or a cube to make it look more like a Euclidean circle or sphere? Well, the internal area or volume will decrease... but the perimeter and area won't. Which means that altering a cube will result in a larger surface area to volume ratio--or, larger surface area for a fixed volume.
So, there you go. The equilibrium, energy-minimizing and surface-area-minimizing shape of a liquid droplet held together by surface tension in a universe operating under the infinity norm must be a cube--and more specifically, an axis-aligned cube.
