Write the binomial expression to be cubed, such as "a + b," in parentheses followed by the power of three: (a + b)^3. This represents cubing the binomial; this will be the left side of the equation.
Cube "a" and place this on the right side of the equation. If "a" is a coefficient with a variable, then cube both the coefficient and the variable. For example, 2x becomes 8x^3, while 5x^2 becomes 125x^8.
Square "a" and multiply the result by 3. Multiply that product by "b" and add this result to the right side of the equation. For example, if "a" is 2x and "b" is 5, the second term would be 2x * 2x * 3 * 5, or 60x^2. The right side of your equation so far would be 8x^3 + 60x^2.
Square "b" and multiply the result by 3. Multiply that product by "a" and add this result to the right portion of the equation. For example, if "a" is 2x and "b" is 5, the third term will be 5 * 5 * 3 * 2x, or 150x.
Add the cube of "b" to the right side. Continuing to follow the example from Steps 3 and 4, if "b" is 5, the last term is 125. Thus, (2x + 5)^3 = 8x^3 + 60x^2 + 150x + 125. Likewise, if the terms were the original "a" and "b," the entire binomial function cubed looks like (a + b)^3 = a^3 + 3ba^2 + 3ab^2 + b^3.