(a+b)^3=a^3+b^3+3ab^2+3a^2b

(a-b)^3=a^3-b^3+3ab^2-3a^2b

2. Cubic sum formula:

a^3+b^3=(a+b)(a^2-ab+b^2)

a^3-b^3=(a-b)(a^2+ab+b^2)

Extended data:

Deduction process:

Given the cube of a number, find the cube of its adjacent number.

Let the adjacent numbers of A be A+ 1 and A- 1, then their cubes can be vividly represented by a three-dimensional figure, as shown in the following figure:

(a+ 1)^3-a^3=(a+ 1)^(3- 1)*a^(3-3)+(a+ 1)^(3-2)*a^(3-2)+(a+ 1)^(3-3)*a^(3- 1)

a^3-(a- 1)^3=a^(3- 1)*(a- 1)^(3-3)+a^(3-2)*(a- 1)^(3-2)+a^(3-3)*(a- 1)^(3- 1)

Geometric understanding is:

A in the long direction and A in the high direction are 1, (A- 1) in the wide direction and A in the high direction are 1, (A- 1) in the long direction and (A- 1) in the wide direction are 65438.

The cubic difference of two non-adjacent numbers p and q can be regarded as the volume difference of the forming volume with the thickness of (P-Q), and the general formula is:

p^3-q^3=[p^(3- 1)*q^(3-3)+p^(3-2)*q^(3-2)+p^(3-3)*q^(3- 1)]*(p-q)

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