**Solution:**

Given equation: X³ - bc = 0

The roots of the equation are α, β, and γ.

Let's solve this problem step by step.

**Step 1: Find the sum of the roots**

The sum of the roots of a cubic equation is given by the formula:

Sum of roots (S) = - (coefficient of X²) / (coefficient of X)

In this case, the coefficient of X² is 0, and the coefficient of X is 0, so the sum of the roots is:

S = -0 / 0 = 0

**Step 2: Find the product of the roots**

The product of the roots of a cubic equation is given by the formula:

Product of roots (P) = (-1)^(number of roots) * (constant term) / (coefficient of X)

In this case, the number of roots is 3, the constant term is -bc, and the coefficient of X is 0, so the product of the roots is:

P = (-1)³ * (-bc) / 0 = -1 * (-bc) / 0 = bc / 0

Since dividing by zero is undefined, we cannot determine the exact value of the product of the roots.

**Step 3: Find the individual roots**

Since the sum of the roots is zero and the product of the roots is undefined, we cannot determine the individual values of α, β, and γ.

**Step 4: Find sin(α)³**

Since we cannot determine the individual values of α, β, and γ, we cannot calculate the value of sin(α)³.

**Conclusion:**

In conclusion, without knowing the values of b and c, we cannot determine the individual roots or the value of sin(α)³ for the given equation.