If a + b = 10 and ab = 21, Find the value of a3 + b3

Given,

$a+b=10, a b=21$

we know that, $(a+b)^{3}=a^{3}+b^{3}+3 a b(a+b) \quad \ldots 1$

substitute $a+b=10, a b=21$ in eq 1

$\Rightarrow(10)^{3}=a^{3}+b^{3}+3(21)(10)$

$\Rightarrow 1000=a^{3}+b^{3}+630$

$\Rightarrow 1000-630=a^{3}+b^{3}$

$\Rightarrow 370=a^{3}+b^{3}$

Hence, the value of $a^{3}+b^{3}=370$