If the density of gold is more than that of iron, why is gold softer than iron?

The softness of a metal is its ability to undergo permanent deformation under applied stress. All metals have specific crystalline structures. Each structure has its own densely packed crystalline planes. There exist line defects and plane defects in a crystal system. Such defects are more in densely packed crystal systems, i.e., metallic crystals with higher density, and result in a number of slip planes, which can easily deform under a little stress. Noble metals like platinum, gold and silver have extra slip planes called twinning. Iron and most of its alloys have very rigid and open packed crystal structures and are difficult to deform.