Which expression is equivalent to

$(2+3)(2^2+3^2)(2^4+3^4)(2^8+3^8)(2^{16}+3^{16})(2^{32}+3^{32})(2^{64}+3^{64})?$

Provide your answer in the form $a^{b} - c^{b}$, and then find the value of $a + b + c$.

Let's think step by step and output the final answer within \boxed{}.
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