I think I found a flaw in Riemann Zeta Function Regularization I think I may have found a flaw in how Zeta Regularization works.
As we all know, it's very famous for proving that $1+2+3+4+...=(-1/12).$ See here

(5 rows of equations at the end of this post)
•On the first row I simply re-define zeta function as a different sigma sum using well established properties of math.
•On the second row I state an identity. Evidence
•On the third row I show $\zeta(-3)$ in the form mentioned on row 1, then via substitution and the identity on row 2 I am able to create a new valid representation of $\zeta(-3)$.
•On row 4 I state that the sum of all real numbers being $-1/12$ as "proven" using Riemann Zeta Function Regularization (see here)
•On row 5 I substitute in the $-1/12$ (from row 4) into the other representation of $\zeta(-3)$ created on row 3. This gives us a final value of $1/144$
The only problem is, for the past 150 years $\zeta(-3) = 1/120$, but now all of a sudden I've made $\zeta(-3) = 1/144$ and as we all know, $120≠144$?
$$
\zeta(s) = \sum_{n=1}^\infty \frac{1}{n^s} = \sum_{n=1}^\infty n^{-s}
$$
$$
\sum_{n=1}^x n^3 = \left( \sum_{n=1}^x n \right)^2
$$
$$
\zeta(-3) = \sum_{n=1}^\infty n^3 = \left( \sum_{n=1}^\infty n \right)^2
$$
$$
\sum_{n=1}^\infty n = -\frac{1}{12}
$$
$$
\frac{1}{120} = \zeta(-3) = \left( - \frac{1}{12} \right)^2 = \frac{1}{144}
$$


The only problem is, for the past 150 years $\zeta(-3) = 1/120$, but now all of a sudden I've made $\zeta(-3) = 1/144$ and as we all know, $120≠144$?

I'm gonna tell you right now the same thing I've told another guy a year or two ago: If you can 
accept that $\infty=\dfrac1{120}$ despite the fact that $\infty\neq\dfrac1{120}$, then you can also accept that $\dfrac1{120}=\dfrac1{144}$ 
despite the fact that $\dfrac1{120}\neq\dfrac1{144}.~$ As boolean logic informs us, a falsehood can imply anything. 
After all, aren't $\dfrac1{120}$ and $\dfrac1{144}$ far closer to one another than either of them is to $\infty$ ? ;-$)$ If you 
have already accepted the bigger lie, what's to stop you from tolerating smaller untruths ? $($On a 
somewhat more serious note, in the holy war against divergent series, self-consistency is often 
the first to fall victim$)$.
