Laying out the math (assuming earth is an homogeneous sphere) just in case it's not clear:

F_gravitational = G m1 m2 /r^2

g = G Mass_earth / r_earth^2

Mass_earth = r_earth^2 * g/G

Density_earth = r_earth^2 * g/G / V_earth

Density_earth = 3*g / (4*Pi*G*r_earth)

Prior to Cavendish we already new g and r_earth, just missing G.