I apologize for the late reply. Calculating volume percentage (φ) is tricky because, as you pointed out, volumes of species with differing densities are not additive. Taking volume (V) as equal to mass (m) divided by density (ρ), the volume ratio of the solute to the solution is

φ_{solute} = (V_{solute}/V_{solution}) = [(m_{solute}/ρ_{solute})/(m_{solution}/ρ_{solution})]

where the solute is HNO_{3} as a pure substance and the solution is nitric acid.

Simplifying,

φ_{solute} = (ρ_{solution}/ρ_{solute})ω_{solute}

where ω is the mass fraction of the solute.

Given ω, the data additionally needed are the density of the pure substance and the solution, both of which can be found in Perry's Chemical Engineers' Handbook. Nitric acid solution densities are available at a wide range of temperatures and mass percentages, but the density of pure HNO_{3} is provided only at 20°C (I was not able to find the density of the pure substance at other temperatures). Kindly note that the density you provided (1.512 g/ml) represents the pure substance and not the 67% solution by weight. Because φ varies with temperature, the calculation with temperatures beyond 20°C will lose accuracy.