The cube-square law was first published by Galileo Galilei in 1638.
You write published which is good (!) because the cube-square law was surely known before Galileo.
I contacted my friend Viktor Blasjo
Certainly much too trivial not have been noticed long before indeed. But I’m not sure about an unequivocal reference off the top of my head. Multiple Greek sources speak of scaling issues of catapults, e.g. how the diameter of the spring or rope of a machine should scale in proportion to the weight of the projectile. An example is:
(The same argument is given in Philon and Heron, pp. 41, 111 of Marsden, E. W. (1971). Greek and Roman artillery: Technical treatises. Oxford: Oxford University Press which unfortunately is not accessible online.)
I’m not sure if this amounts the law you mention exactly. But all of these sources are clearly interested in this because it leads to the mathematically interesting problem of cube duplication. So clearly the Greeks had thought a lot about scaling and this is the part preserved in the record because of its associated technical mathematical machinery.
You write published which is good (!) because the cube-square law was surely known before Galileo.
I contacted my friend Viktor Blasjo