Will density of a metal increases during forging? This question is metallurgical engineering, but I had a similar doubt regarding density of liquids and what causing it.
Forged parts refines defects, dislocations will be moved strengthening the metal. But will the density of forged metal change?
My earlier question was, what causes liquids to have different densities?
 A: The answer is that in principle yes, the removal of defects will increase the density. The question is by how much.
You specifically ask about forging. The forging process doesn't remove dislocations but instead moves them until they become pinned, which is what causes the work hardening. Well, that's an oversimplification since some defects will be removed but on the other hand fresh defects will be created. So whether forging will change the density, and if so by how much, is a hard question to answer.
The extreme version of removing defects would be to compare the densities of crystalline and amorphous metal. However I'm not sure that the common metals can be prepared in well characterised amorphous forms. If you compare that most common of amorphous solids, silica glass, then the density of the amorphous form is about 10% lower than the density of quartz.
I did have a Google for the effect of forging on density (I'm sure you did too) but I couldn't find anything that looked reliable. I did find this paper that reports a density decrease, but the authors suggest this is due to formation of small cracks. I think it would be a hard experiment to do as there are other variables that are hard to control.
A: The density of the metal, steel in this case, is a function of atomic weight, atomic spacing, and the volume of steel being measured.  Since atoms in the metal crystal (no, there are no molecules in ordinary steel) are very small, it would take a huge change in the inter-atomic spacing to affect density to a measureable degree.  The change would have to affect the strength of the bonds that hold the atoms together (and apart) and this is not easily changed by conventional physical means.  The simpler answer is: No, forging does not change the density of the metal.
A: Forging inevitably compresses the mass and therefore increases the density. In a perfect metal, forging would make little or no difference but no metals are perfect and most contain unwanted substances and voids. During the forging process voids are compressed and it is also possible that the impurities also are diminished in size depending on what they are. The difference in density may well be very small.
