Calculating the volume of 1 mole of liquid water
The molecule length value you are using is the problem. It is more like 300 pm, which is the van der Vaals diameter and includes regions where electron density is significant. You have calculated an internuclear distance, but the nuclei of one molecule won't come close to those of another molecule because of electron-electron repulsion.

This will change your answer by a factor of 8.

See Finney, J. L. The water molecule and its interactions: the interaction between theory, modelling, and experiment. J. Mol. Liq. 2001, 90 (1-3), 303–312. DOI: 10.1016/S0167-7322(01)00134-9.