Choice A is correct. It's given that the sample is in the shape of a cube with edge lengths of $0.9$ meters. Therefore, the volume of the sample is $0,90^3$, or $0.729$, cubic meters. It's also given that the sample has a density of $807$ kilograms per $1$ cubic meter. Therefore, the mass of this sample is $0.729 cubic meters(\dfrac{807 kilograms}{1 cubic meter})$, or $588.308$ kilograms. Rounding this mass to the nearest whole number gives $588$ kilograms. Therefore, to the nearest whole number, the mass, in kilograms, of this sample is $588$.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.