Evaluate the expression \( 2 b^{3}+5 \) when \( b=3 \). \( 2 b^{3}+5=2(\sqrt{2 \pi})^{3}+5 \)

To evaluate the expression \( 2 b^{3}+5 \) when \( b=3 \), we first substitute \( b \) with 3: \[ 2(3)^{3}+5 \] Calculating \( 3^{3} \): \[ 3^{3} = 27 \] Now substitute that back into the expression: \[ 2(27)+5 \] Next, multiply: \[ 2 \times 27 = 54 \] Finally, add 5: \[ 54 + 5 = 59 \] Hence, the evaluated expression is \( 59 \). Now, for the other expression \( 2(\sqrt{2 \pi})^{3}+5 \), let's evaluate it: First, calculate \( (\sqrt{2 \pi})^{3} \): \[ (\sqrt{2 \pi})^{3} = (2 \pi)^{3/2} = 2^{3/2} \cdot \pi^{3/2} = 2\sqrt{2} \cdot \pi^{3/2} \] Substituting this into the expression: \[ 2(2 \sqrt{2} \cdot \pi^{3/2}) + 5 = 4 \sqrt{2} \cdot \pi^{3/2} + 5 \] This is our evaluated expression based on the other input for \( b \).