Final answer:
A cell most likely contains the most nucleotides at the end of the S phase and during the G2 phase, as DNA replication during the S phase doubles the nucleotides, preparing the cell for mitosis.
Step-by-step explanation:
The cell will most likely contain the most nucleotides at the end of the Synthesis Phase (S) and throughout the G2 phase of the cell cycle. During the S phase, DNA replication occurs, which doubles the number of nucleotides in the cell, as the DNA content effectively doubles.
Following the S phase, the cell enters the G2 phase, during which the cell prepares for mitosis and still contains the heightened amount of nucleotides because replication has just occurred. Moreover, one of the prerequisites for clearance at the G2 checkpoint is an adequate stockpile of nucleotides confirming that high nucleotide content is critical at this stage to proceed to mitosis.