How do I prove/disprove this??

The equality doesn't hold for some $b$. With $b = 1$, we have \begin{align*} & \left(\sum_{k=0}^{2b-1} \left(\prod_{j=1}^4(4b-k+j)\right)\right)+\left(\prod_{j=1}^4(2b+j)\right)-(2b+1)\left(\prod_{j=1}^3(2b+j)\right) \\ = \: & \left(\sum_{k=0}^{1} \left(\prod_{j=1}^4(4-k+j)\right)\right)+\left(\prod_{j=1}^4(2+j)\right)-3\left(\prod_{j=1}^3(2+j)\right) \\ = \: &\left(\prod_{j=1}^4(4-0+j) + \prod_{j=1}^4(4-1+j) \right) + (3 \cdot 4 \cdot 5 \cdot 6) - 3 \cdot (3 \cdot 4 \cdot 5) \\ = \: &\left(5 \cdot 6 \cdot 7 \cdot 8+ 4 \cdot 5 \cdot 6 \cdot 7\right) + (3 \cdot 4 \cdot 5 \cdot 6) - 3 \cdot (3 \cdot 4 \cdot 5) \\ = \: & 1680 + 840 + 360 - 180 \\ = \: & 2700, \end{align*} while $2(2b+1)^2(2b+2)^2 = 2 \cdot 3^2 \cdot 4^2 = 288$.