we have the equation
(3a^3 - 5b^3) + ____x_ a^3 + ____y_ b^3 = (a^3 + b^3)
where
x and y are the missing coefficients
xa^3+yb^3= (a^3 + b^3)-(3a^3 - 5b^3)
xa^3+yb^3=a^3+b^3-3a^3+5b^3
Combine like terms in the right side
xa^3+yb^3=-2a^3+6b^3
so
Compare like terms
xa^3=-2a^3 -------> x=-2
yb^3=6b^3 ------> y=6
therefore
The answer is
-2 and 6