# Sum of Cubes

## Reference > Algebra: Sums and Differences of Squares and Cubes

 DescriptionThe Sum of Cubes Rule states that:$${a}^{3}+{b}^{3}=(a+b)({a}^{2}-ab+{b}^{2})$$
 Examples${8x}^{3}+27$1 Rewrite it in the form $${a}^{3}+{b}^{3}$$, where $$a=2x$$ and $$b=3$$.${(2x)}^{3}+{3}^{3}$2 Use Sum of Cubes: $${a}^{3}+{b}^{3}=(a+b)({a}^{2}-ab+{b}^{2})$$.$(2x+3)({(2x)}^{2}-(2x)(3)+{3}^{2})$3 Use Multiplication Distributive Property: $${(xy)}^{a}={x}^{a}{y}^{a}$$.$(2x+3)({2}^{2}{x}^{2}-2x\times 3+{3}^{2})$4 Simplify  $${2}^{2}$$  to  $$4$$.$(2x+3)(4{x}^{2}-2x\times 3+{3}^{2})$5 Simplify  $${3}^{2}$$  to  $$9$$.$(2x+3)(4{x}^{2}-2x\times 3+9)$6 Simplify  $$2x\times 3$$  to  $$6x$$.$(2x+3)(4{x}^{2}-6x+9)$Done(2*x+3)*(4*x^2-6*x+9)