concentration of only [B] is increased three times?

The rate law is $\text{Rate} = k[\text{A}][\text{B}]^2$. When $[\text{B}]$ is increased three times: $\text{Rate}' = k[\text{A}](3[\text{B}])^2 = 9 k[\text{A}][\text{B}]^2 = 9 \times \text{Rate}$ The rate of reaction increases by 9 times (becomes 9 times the initial rate).