Solution: Use identity $ a^3 + b^3 = (a + b)^3 - 3ab(a + b) $. First find $ ab $: $ (a + b)^2 = a^2 + 2ab + b^2 \Rightarrow 49 = 35 + 2ab \Rightarrow ab = 7 $. Then $ a^3 + b^3 = 343 - 3 \cdot 7 \cdot 7 = 343 - 147 = \boxed196 $. - Abu Waleed Tea