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As a,b,c,d are odd perfect cube
then cube root of a,b,c,d will also be a odd number
hence
![\sqrt[3]{a} \: and \: \sqrt[3]{b} \: are \: odd \\ \\ \sqrt[3]{a} + \sqrt[3]{b} \: is \:even \: \\ as \: sum \: of \: two \: odd \: number \: is \: always \: even \\ hence \: it \: will \: have \: 2 \: as \: a \: factor \\ now \: squaring \: it \: will \: give \: 4 \: as \: a \: factor \\ similarly \\ \sqrt[3]{c} + \sqrt[3]{d} is \: even \\ hence \: it \: will \: also \: has \: 2 \: as \: a \: factor \\ multiplying \\ you \: get \\ 4 \times 2 = 8 \: as \: a \: factor](https://tex.z-dn.net/?f=+%5Csqrt%5B3%5D%7Ba%7D++++%5C%3A+and+%5C%3A++%5Csqrt%5B3%5D%7Bb%7D++%5C%3A+are+%5C%3A+odd+%5C%5C++%5C%5C++++%5Csqrt%5B3%5D%7Ba%7D++%2B+++%5Csqrt%5B3%5D%7Bb%7D++%5C%3A+is+%5C%3Aeven+%5C%3A++%5C%5C+as+%5C%3A+sum+%5C%3A+of+%5C%3A+two+%5C%3A+odd+%5C%3A+number+%5C%3A+is+%5C%3A+always+%5C%3A+even+%5C%5C+hence+%5C%3A+it+%5C%3A+will+%5C%3A+have+%5C%3A+2+%5C%3A+as+%5C%3A+a+%5C%3A+factor+%5C%5C+now+%5C%3A+squaring+%5C%3A+it+%5C%3A+will+%5C%3A+give+%5C%3A+4+%5C%3A+as+%5C%3A+a+%5C%3A+factor+%5C%5C+similarly+%5C%5C+++%5Csqrt%5B3%5D%7Bc%7D++%2B++%5Csqrt%5B3%5D%7Bd%7D+is+%5C%3A+even+%5C%5C+hence+%5C%3A+it+%5C%3A+will+%5C%3A+also+%5C%3A+has+%5C%3A+2+%5C%3A+as+%5C%3A+a+%5C%3A+factor+%5C%5C+multiplying+%5C%5C+you+%5C%3A+get+%5C%5C+4+%5Ctimes+2+%3D+8+%5C%3A+as+%5C%3A+a+%5C%3A+factor "\sqrt[3]{a} \: and \: \sqrt[3]{b} \: are \: odd \\ \\ \sqrt[3]{a} + \sqrt[3]{b} \: is \:even \: \\ as \: sum \: of \: two \: odd \: number \: is \: always \: even \\ hence \: it \: will \: have \: 2 \: as \: a \: factor \\ now \: squaring \: it \: will \: give \: 4 \: as \: a \: factor \\ similarly \\ \sqrt[3]{c} + \sqrt[3]{d} is \: even \\ hence \: it \: will \: also \: has \: 2 \: as \: a \: factor \\ multiplying \\ you \: get \\ 4 \times 2 = 8 \: as \: a \: factor")
hence 8 will always be the factor of given expression
then cube root of a,b,c,d will also be a odd number
hence
hence 8 will always be the factor of given expression
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