There are two principles at play here: a mathematical principle that favors hexagonal networks, and a physical principle that favors a network with straight walls.
The mathematical principle that prefers hexagonal planar networks is Euler's theorem applied to the two-torus $\mathbb{T}^2$ (to avoid boundary effects), $$V-E+F=0,$$ with $V$ the number of vertices, $E$ the number of edges, and $F$ the number of cells. Because every vertex is incident with three edges$^\ast$ and every edge is incident with two vertices, we have $2E = 3V$, hence $E/F=3$. Since every edge is adjacent to two cells, the average number of sides per cell is 6 --- hence a uniform network must be hexagonal.
$^\ast$ A vertex with a higher coordination number than 3 is mechanically unstable, it will split as indicated in this diagram to lower the surface energy.
blue: total edge length for the left diagram (diagonals of a unit square), gold: total edge length for the right diagram, as a function of the length $x$ of the splitting.
Euler's theorem still allows for curved rather than straight walls of the cells. The physical principle that prefers straight walls is the minimization of surface area.
source: Honeybee combs: how the circular cells transform into rounded hexagons
An experiment that appears to be directly relevant for honeybee combs is the transformation of a closed-packed bundle of circular plastic straws into a hexagonal pattern on heating by conduction until the melting point of the plastic. Likewise, the honeybee combs start out as such a closed-packed bundle of circular cells (panel a). The wax walls of the cells are heated to the melting point by the bees and then become straight to reduce the surface energy (panel b).