If a^3 - b^3 = 625, a^2 - b^2 = 25 and a + b = 5 then the value of a^2 + ab + b^2 is:

a² − b² = (a − b)(a + b) = 25 with a + b = 5, so a − b = 5. Then a³ − b³ = (a − b)(a² + ab + b²) = 625 gives a² + ab + b² = 625/5 = 125.