To solve this problem, we need to analyze the condition of orthogonality between two families of circles, specifically those that intersect a family of circles passing through fixed points $A = (2, 1)$ and $B = (4, 3)$.

1. Equation of the Family of Circles Passing Through $A$ and $B$: Any circle passing through two fixed points $A$ and $B$ can be represented as: $S = 0 \Rightarrow (x - 2)^2 + (y - 1)^2 + \lambda \left[(x - 4)^2 + (y - 3)^2 \right] = 0$ where $\lambda$ is a parameter.

2. Orthogonality Condition: For a circle to intersect another family of circles orthogonally, the sum of their gradients at any intersection point must be zero. The condition for orthogonality between two circles with equations $S = 0$ and $T = 0$ is given by: $2g g' + 2f f' = c + c'$ where $g, f,$ and $c$ are the coefficients in the general form of a circle $x^2 + y^2 + 2gx + 2fy + c = 0$.

3. Determine the Fixed Points $(x_1, y_1)$ and $(x_2, y_2)$: Since the circles are orthogonal to the family passing through $A$ and $B$, they must pass through the points where this family intersects the line at infinity, leading us to a fixed pair of points, which can often include complex values if no real intersection exists.

4. Calculate $(x_1^3 + x_2^3 + y_1^3 + y_2^3)$: The values of $x_1, x_2, y_1,$ and $y_2$ would be determined by solving the orthogonal condition explicitly, which may reveal real or complex roots.

Given these conditions, a detailed solution would involve either directly computing the values of $x_1, x_2, y_1,$ and $y_2$ or deducing them based on symmetry properties.