\(a)x^2+14x+49=x^2+2\cdot x\cdot7+7^2=\left(x+7\right)^2\\ b)x^2-8x+16=x^2-2\cdot x\cdot4+4^2=\left(x-4\right)^2\\ c)x^3-6x^2+12x-8=x^3-3\cdot x^2\cdot2+3\cdot x\cdot2^2-2^3=\left(x-2\right)^3\\ d)36x^2+36x+9=\left(6x\right)^2+2\cdot6x\cdot3+3^2=\left(6x+3\right)^2\\ e)\left(x+3\right)\left(x^2-3x+9\right)=x^3+3^3=x^3+27\\ f)x^3+1=\left(x+1\right)\left(x^2-x\cdot1+1^2\right)=\left(x+1\right)\left(x^2-x+1\right)\)