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The easiest way to find a trinomial where $8x^2y^3$ is the greatest common factor is to first find a trinomial with no common factors and then multiply it by $8x^2y^3$. Thus, we find:
$$8x^2y^3\left(8x^2+5x+3\right) \\ 8\cdot \:8x^2x^2y^3+8\cdot \:5x^2xy^3+8\cdot \:3x^2y^3 \\ 64x^4y^3+40x^3y^3+24x^2y^3$$
