(a+ b)³ = a³ + 3a²b + 3ab² + b³ = (a³ + 3ab²) + (b³ + 3a²b) = 2006 + 2005 = 4011

=> a + b = \(\sqrt[3]{4011}\)

(a - b)³ = a³ - 3a²b + 3ab² - b³ = (a³ + 3ab²) - (b³ + 3a²b) = 2006 - 2005 = 1

=> a - b = 1

=> P = a² - b² = (a - b)(a + b) = \(\sqrt[3]{4011}\)