Final answer:
The nucleus would contain 6 picograms of DNA in the late S phase or G2 phase of the cell cycle, as DNA content doubles following replication during these stages.
Step-by-step explanation:
If the DNA content in a nucleus of a population of yeast cells ranges from 3 to 6 picograms, the stage of the cell cycle in which the nucleus would contain 6 picograms of DNA is likely the G2 phase or late S phase. This is because, during the S phase, DNA replicates, doubling its content in preparation for cell division. By the end of the S phase and entering G2, the cell has twice the amount of DNA, which would be consistent with the observed increase to 6 picograms.