Verifying the constant elasticity of the demand model Q= aP^b "It is well known" that the elasticity of $Q$ relative to $P$ is the constant $b$ in the equation $Q(P)=aP^b$. We can verify it using the convenient definition of elasticity $= \frac{dQ}{dP} \frac{P}{Q}$, we can verify it in Wikipedia.

Based on this, when I create a spreadsheet with parameters $b=-2$, $a=100$ and P ranging from 1-5 by 1 I expected to recover an elasticity of -2, where elasticity =  % change in Q/ % change in P.  This is not the case. Instead the elasticity  varies substantially as the % change in P varies.

I'm forced to conclude that 'constant elasticity' does not mean a fixed value regardless of the magnitude of the price change, but only invariant with regards to the value of price OR that I have a spreadsheet error.

I've pasted an image of the spreadsheet results below.  Obviously, without seeing the formulas, no one can verify that I don't have an error, but I'm hopeful that someone will give this a spin for themselves and get very different numbers and then I'll know my failure to verify the constant elasticity in this function is a spreadsheet error.
The problem with your calculations is that you have very big changes in price   

If you made price increases of $1\%$ in price, you would find the quantity fell by about $2\%$ as shown in the table below leading to an elasticity of about $-2$  

If you made the price changes even smaller, the calculated elasticity would get even closer to $2$, and in a sense you are looking for the limit of elasticity as the price change approaches $0$, which will indeed be the constant $b=-2$

 a       b      P       Q=a*P^b pct change Q    pct change P   elasticity

100     -2      1       100.00          
100     -2      1.01     98.03      -1.97%          1%          -1.97
100     -2      2        25.00          
100     -2      2.02     24.51      -1.97%          1%          -1.97
100     -2      3        11.11          
100     -2      3.03     10.89      -1.97%          1%          -1.97
100     -2      4         6.25          
100     -2      4.04      6.13      -1.97%          1%          -1.97
100     -2      5         4.00          
100     -2      5.05      3.92      -1.97%          1%          -1.97