\(\left(2x+3\right)^3-4\left(x-2\right)^3\)
\(=2x^3+3.2x^2.3+3.2x.3^2+3^3-\left(4x-8\right)^3\)
\(=2x^3+18x^2+54x+27-\left(4x-8\right)^3\)
\(=2x^3+18x^2+54x+27-\left(4x^3+3.4x^2.8+3.4x.8^2+8^3\right)\)
\(=2x^3+18x^2+54x+27-4x^3-96x^2-768x-512\)
\(=\left(2x^3-4x^3\right)+\left(18x^2-96x^2\right)+\left(54x-768x\right)+\left(27-512\right)\)
\(=-2x^3-78x^2-714x-485\)