Derivation of Electric Field with Gauss's Law

[k_squared]

I did everything I could to solve the following problem:
A solid ball of radius r_b has a uniform charge density ρ.

What is the magnitude of the electric field E(r) at a distance r>r_b from the center of the ball?
E(r) =

My third attempt went like this: q_encl=[ρ(4/3)(π)r_b³]

EV=[ρ(4/3)(π)r_b³]/(ε₀)
E(4/3)πr³=[ρ(4/3)(π)r_b³]/(ε₀)

And ah, well, a little simple division and cancelling leads to:
[ρr_b³/[ε₀r³]

However, the book answer is 1/3 my answer. Could someone please tell me where this constant develops?

 

[Khashishi]

Try Gauss's law. Start by writing the equation for Gauss's law.

 

[vela]

EV=[ρ(4/3)(π)r_b³]/(ε₀)

The righthand side is okay. Check the details on the lefthand side of this equation.

 

[Chandra Prayaga]

Why did you multiply the electric field with the volume?