No, the density of an object does not depend on its size.
A piece of glass with a volume of 10 cm³ may have a mass of 27 g. Its density is
D = m/V = 27 g/10 cm³ = 2.7 g/cm³
A piece of the same type of glass with a volume of 20 cm³ will have a mass
of 54 g. Its density is
D = m/V = 54 g/20 cm³ = 2.7 g/cm³
Thus, density does not change with the size of an object. Density is an intensive property.