TOPAS-nBio was used to simulate, collision-to-collision, the complete trajectories of electrons in water generated during the explicit simulation of 64Cu decay. S-values and direct damage to the DNA were calculated representing the cell (C) and the cell nucleus (N) with concentric spheres of 5 μm and 4 μm in radius, respectively. The considered "target"←"source" configurations, including the cell surface (Cs) and cytoplasm (Cy), were: C←C, C←Cs, N←N, N←Cy and N←Cs. Ionization cluster size distributions were also calculated in a cylinder immersed in water corresponding to a DNA segment of 10 base-pairs in length (diameter 2.3 nm, length 3.4 nm), modeling a radioactive point source moving from the central axis to the edge of the cylinder. For that, the first moment (M1) and cumulative probability of having a cluster size of 2 or more ionizations in the cylindrical volume (F2) were obtained. Finally, the direct damage to the DNA was estimated by quantifying double-strand breaks (DSBs) using the clustering algorithm DBSCAN. The S-values obtained with TOPAS-nBio for 64Cu were 7.879x10-4±5x10-7, 4.351x10-4±6x10-7, 1.442x10-3±1x10-6, 2.596x10-4±8x10-7, 1.127x10-4±4x10-7 Gy/Bq-s for the configurations C←C, C←Cs, N←N, N←Cy and N←Cs, respectively. The difference of these values, compared with previously reported S-values for 64Cu with the code MNCP and software MIRDCell, ranged from -4% to -25% for the configurations N←N and N←Cs, respectively. On the other hand, F2 was maximum with the source at the center of the cylinder 0.373±0.001, and monotonically decreased until reaching a value of 0.058±0.001 at 2.3 nm. The same behavior was observed for M1 with values ranging from 2.188±0.004 to 0.242±0.002. Finally, the DBSCAN algorithm showed that the mean number of DNA DSBs per decay were 0.187±0.001, 0.0317±0.0005, and 0.0125±0.0002 DSB-(Bq-s)-1 for the configurations N←N, N←Cs, and N←Cy, respectively. In conclusion, the results of the S-values show that the absorbed dose strongly depends on the distribution of the radionuclide in the cell, the dose being higher when 64Cu is internalized in the cell nucleus, which is reinforced by the nanodosimetric study by the presence of DNA DSBs attributable to the Auger electrons emitted during the decay of 64Cu.