The Perfect Cuboid problem was being considered in the early 18th century (according to http://mathworld.wolfram.com/EulerBrick.htmlhttps://mathworld.wolfram.com/EulerBrick.html )
I don't know if any ancient Greeks are on record as having considered the problem; but that doesn't seem beyond the bounds of possibility, although I would guess that in those times they were preoccupied mostly with 2-D problems.