Sum and difference of cubes worksheet

Two formulas that students mix up constantly, because the only difference between them is where the minus signs go. Tick one pattern to drill it, or both to make them decide which is which.

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Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Sum and Difference of Cubes Date Period Factor each completely. $64 a^{3} - 125$ $27 b^{3} + 64$ $64 p^{3} - 27$ $8 p^{3} + 27$ $8 b^{3} - 27$ $27 x^{3} + 125$ $27 b^{3} - 64$ $27 r^{3} + 64$ $27 r^{3} - 125$ $8 y^{3} + 125$ $8 n^{3} - 27$ $27 b^{3} + 8$ $64 b^{3} - 125$ $64 y^{3} + 125$ $8 k^{3} - 125$ $27 p^{3} + 64$ $64 x^{3} - 125$ $8 b^{3} + 27$ $27 k^{3} - 64$ $8 m^{3} + 27$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Sum and Difference of Cubes

Date Period

Factor each completely.

$64 a^{3} - 125$
$27 b^{3} + 64$
$64 p^{3} - 27$
$8 p^{3} + 27$
$8 b^{3} - 27$
$27 x^{3} + 125$
$27 b^{3} - 64$
$27 r^{3} + 64$
$27 r^{3} - 125$
$8 y^{3} + 125$
$8 n^{3} - 27$
$27 b^{3} + 8$
$64 b^{3} - 125$
$64 y^{3} + 125$
$8 k^{3} - 125$
$27 p^{3} + 64$
$64 x^{3} - 125$
$8 b^{3} + 27$
$27 k^{3} - 64$
$8 m^{3} + 27$



Sigma Prep · sigmaprep.io/worksheets Name Sum and Difference of CubesAnswer keyVersion 1 Date Period Factor each completely. $64 a^{3} - 125$ $(4 a - 5) (16 a^{2} + 20 a + 25)$ $27 b^{3} + 64$ $(3 b + 4) (9 b^{2} - 12 b + 16)$ $64 p^{3} - 27$ $(4 p - 3) (16 p^{2} + 12 p + 9)$ $8 p^{3} + 27$ $(2 p + 3) (4 p^{2} - 6 p + 9)$ $8 b^{3} - 27$ $(2 b - 3) (4 b^{2} + 6 b + 9)$ $27 x^{3} + 125$ $(3 x + 5) (9 x^{2} - 15 x + 25)$ $27 b^{3} - 64$ $(3 b - 4) (9 b^{2} + 12 b + 16)$ $27 r^{3} + 64$ $(3 r + 4) (9 r^{2} - 12 r + 16)$ $27 r^{3} - 125$ $(3 r - 5) (9 r^{2} + 15 r + 25)$ $8 y^{3} + 125$ $(2 y + 5) (4 y^{2} - 10 y + 25)$ $8 n^{3} - 27$ $(2 n - 3) (4 n^{2} + 6 n + 9)$ $27 b^{3} + 8$ $(3 b + 2) (9 b^{2} - 6 b + 4)$ $64 b^{3} - 125$ $(4 b - 5) (16 b^{2} + 20 b + 25)$ $64 y^{3} + 125$ $(4 y + 5) (16 y^{2} - 20 y + 25)$ $8 k^{3} - 125$ $(2 k - 5) (4 k^{2} + 10 k + 25)$ $27 p^{3} + 64$ $(3 p + 4) (9 p^{2} - 12 p + 16)$ $64 x^{3} - 125$ $(4 x - 5) (16 x^{2} + 20 x + 25)$ $8 b^{3} + 27$ $(2 b + 3) (4 b^{2} - 6 b + 9)$ $27 k^{3} - 64$ $(3 k - 4) (9 k^{2} + 12 k + 16)$ $8 m^{3} + 27$ $(2 m + 3) (4 m^{2} - 6 m + 9)$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Sum and Difference of CubesAnswer keyVersion 1

Date Period

Factor each completely.

$64 a^{3} - 125$ $(4 a - 5) (16 a^{2} + 20 a + 25)$
$27 b^{3} + 64$ $(3 b + 4) (9 b^{2} - 12 b + 16)$
$64 p^{3} - 27$ $(4 p - 3) (16 p^{2} + 12 p + 9)$
$8 p^{3} + 27$ $(2 p + 3) (4 p^{2} - 6 p + 9)$
$8 b^{3} - 27$ $(2 b - 3) (4 b^{2} + 6 b + 9)$
$27 x^{3} + 125$ $(3 x + 5) (9 x^{2} - 15 x + 25)$
$27 b^{3} - 64$ $(3 b - 4) (9 b^{2} + 12 b + 16)$
$27 r^{3} + 64$ $(3 r + 4) (9 r^{2} - 12 r + 16)$
$27 r^{3} - 125$ $(3 r - 5) (9 r^{2} + 15 r + 25)$
$8 y^{3} + 125$ $(2 y + 5) (4 y^{2} - 10 y + 25)$
$8 n^{3} - 27$ $(2 n - 3) (4 n^{2} + 6 n + 9)$
$27 b^{3} + 8$ $(3 b + 2) (9 b^{2} - 6 b + 4)$
$64 b^{3} - 125$ $(4 b - 5) (16 b^{2} + 20 b + 25)$
$64 y^{3} + 125$ $(4 y + 5) (16 y^{2} - 20 y + 25)$
$8 k^{3} - 125$ $(2 k - 5) (4 k^{2} + 10 k + 25)$
$27 p^{3} + 64$ $(3 p + 4) (9 p^{2} - 12 p + 16)$
$64 x^{3} - 125$ $(4 x - 5) (16 x^{2} + 20 x + 25)$
$8 b^{3} + 27$ $(2 b + 3) (4 b^{2} - 6 b + 9)$
$27 k^{3} - 64$ $(3 k - 4) (9 k^{2} + 12 k + 16)$
$8 m^{3} + 27$ $(2 m + 3) (4 m^{2} - 6 m + 9)$

How to do these

$x^{3} - 27$

Both terms are cubes: x³ and 3³.
The first parenthesis copies the sign: (x - 3).
The second is x² + 3x + 9, with the middle sign flipped.

The answer is $(x - 3) (x^{2} + 3 x + 9)$ .

Where students go wrong

Two things. The signs: in the second parenthesis the middle term always has the opposite sign to the first parenthesis, so a difference of cubes gives a plus in the middle and a sum gives a minus. And students try to keep factoring x² + 3x + 9. It never factors, on any of these, so the answer is finished.

Also called the sum of cubes, the difference of cubes or cube factoring formulas.

What you can put on this worksheet

A difference of cubes: $v^{3} - 64$ → $(v - 4) (v^{2} + 4 v + 16)$
A sum of cubes: $v^{3} + 64$ → $(v + 4) (v^{2} - 4 v + 16)$

Questions about these worksheets

Yes. Every sum and difference of cubes sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 2 is usually taken around 10th or 11th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the sum and difference of cubes questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 2: a difference of cubes and a sum of cubes. Tick as many as you want and set how many of each, or let it spread them evenly.

Sum and difference of cubes worksheet

Select your difficulty

Sum and Difference of Cubes

Sum and Difference of CubesAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

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