What is the general formula for the sum of cubes?

The correct choice for the general formula for the sum of cubes is indeed derived from the identity that expresses the sum of two cubes, which states:

[ a^3 + b^3 = (a + b)(a^2 - ab + b^2). ]

This formula highlights how the sum of cubes can be expressed in a factored form. The first part, ((a + b)), represents the sum of the two numbers whose cubes are being added, while the second part, ((a^2 - ab + b^2)), provides a polynomial that captures the relationship between (a) and (b).

When applied, this formula is useful because it allows for simplification and factorization in algebraic expressions and can help in solving equations or simplifying calculations involving cubes.

The option that uses a minus sign in the middle term of the polynomial, as in ((a + b)(a^2 - ab + b^2)), accurately reflects the mathematical principle at hand, thus confirming its correctness as the appropriate sum of cubes formula.