Euler Four-Square Identity -- from Wolfram MathWorld

The amazing polynomial identity communicated by Euler in a letter to Goldbach on April 12, 1749 (incorrectly given as April 15, 1705--before Euler was born--in Conway and Guy 1996, p. 232). The identity also follows from the fact that the norm of the product of two quaternions is the product of the norms (Conway and Guy 1996).

Euler Formula -- from Wolfram MathWorld

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Euler Polynomial -- from Wolfram MathWorld

PDF) Taylor's series expansions for real powers of two functions

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Degen's Eight-Square Identity -- from Wolfram MathWorld

Where have I gone wrong with this deduction. I know, (e^(x))^2

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