concentration of both [A] and [B] is doubled?

When both $[\text{A}]$ and $[\text{B}]$ are doubled: $\text{Rate}' = k(2[\text{A}])(2[\text{B}])^2 = 8 k[\text{A}][\text{B}]^2 = 8 \times \text{Rate}$ The rate of reaction increases by 8 times (becomes 8 times the initial rate).