You have said that 15cm³ of gold weighs 2.8N. So I may infer that each cm³
of gold weighs about 0.19N. When I compare that figure with the 0.13N per cm³
of mercury, it becomes immediately apparent that the gold is more dense than
mercury. Therefore, the sample of gold, no matter what its size or weight, will
displace its total volume of mercury, and will go on to sink entirely beneath the
waves in the mercury.