We are tasked with finding values of $a$, $b$, $c$, and $d$ for the cubic equation $y = ax^3 + bx^2 + cx + d$ such that it passes through the points $(1, 0)$, $(2, 1)$, and $(3, 2)$.

Let's solve this step by step.

Step 1: Substituting the points into the equation.

The cubic equation is:

$y = ax^3 + bx^2 + cx + d$

Substituting the points $(1,0)$, $(2,1)$, and $(3,2)$ will give us a system of linear equations.

1. For the point $(1, 0)$: $0 = a(1)^3 + b(1)^2 + c(1) + d \quad \Rightarrow \quad a + b + c + d = 0$

2. For the point $(2, 1)$: $1 = a(2)^3 + b(2)^2 + c(2) + d \quad \Rightarrow \quad 8a + 4b + 2c + d = 1$

3. For the point $(3, 2)$: $2 = a(3)^3 + b(3)^2 + c(3) + d \quad \Rightarrow \quad 27a + 9b + 3c + d = 2$

Now, we have the following system of equations: