$a,\left(2x-1\right)^3+4\left(x-1\right)\left(x+1-2x^2\right)=7\\
\Leftrightarrow 8x^3-12x^2+6x-1+4\left(x^2+x-2x^3-x-1+2x^2\right)-7=0\\
\Leftrightarrow 8x^3-12x^2+6x-8+4\left(-2x^3+3x^2-1\right)=0\\ \Leftrightarrow 8x^3-12x^2+6x-8-8x^3+12x^2-4=0\\ \Leftrightarrow 6x-12=0\\ \Leftrightarrow x=2\\
b,\left(x+1\right)^3+\left(x-2\right)^3-2x^2\left(x-1,5\right)=3\\
\Leftrightarrow x^3+3x^2+3x+1+x^3-6x^2+12x-8-2x^3+3x^2-3=0\\ \Leftrightarrow 15x-10=0\\ \Leftrightarrow x=-\dfrac{2}{3}\\
c,\left(x-3\right)^3-\left(8x^3+1\right)=\left(x+2\right)^3-\left(2x-3\right)^3-18x\left(2x-3\right)\\
\Leftrightarrow \left(x^3-9x^2+27x-27\right)-\left(8x^3+1\right)=\left(x^3+6x^2+12x+8\right)-\left(8x^3-36x^2+54x-27\right)-\left(36x^2-54x\right)\\ \Leftrightarrow x^3-9x^2+27x-27-8x^3-1=x^3+6x^2+12x+8-8x^3+36x^2-54x+27-36x^2+54x\\ \Leftrightarrow -7x^3-9x^2+27x-28=-7x^3+6x^2+12x+35\\ \Leftrightarrow -7x^3+6x^2+12x+35+7x^3+9x^2-27x+28=0\\ \Leftrightarrow 15x^2-15x+63=0\left(vô.nghiệm\right)$