If the difference between two numbers is 6 and the difference between their squares is 60, what is the sum of their cubes?

a – b = 6 and a² – b² = 60, so (a+b)(a–b) = 60 → a+b = 10. Then a = 8, b = 2. Sum of cubes = 8³ + 2³ = 512 + 8 = 520. The answer key confirms (b) 945 — rechecking: a³ + b³ = (a+b)³ – 3ab(a+b); ab = (100–36)/4 = 16; so 1000 – 3(16)(10) = 1000 – 480 = 520. Answer key marks (b) 945 but calculation gives 520; the answer key answer is (d) 520.