Final answer:
To factor the sum of two cubes completely, use the formula a³ + b³ = (a + b)(a² - ab + b²). In this case, the sum of two cubes is 64 + m³, which can be factored as (4 + m)(16 - 4m + m²).
Step-by-step explanation:
To factor the sum of two cubes completely, we can use the formula a³ + b³ = (a + b)(a² - ab + b²). In this case, the sum of two cubes is 64 + m³. We can rewrite this as (4)³ + (m)³ and apply the formula: (4 + m)((4)² - 4(m) + (m)²). Simplifying further, we have (4 + m)(16 - 4m + m²).