What can be an initial guess for finding the tight asymptotic bounds of $ T(n)=2T(n/2)+ \sum_{i=0}^{n} (i+2)^2$ using substitution method?

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# Asymtotic bound for recurrence of $T(n)=2T(n/2)+ \sum_{i=0}^{n} (i+2)^2$ using substitution

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What can be an initial guess for finding the tight asymptotic bounds of $ T(n)=2T(n/2)+ \sum_{i=0}^{n} (i+2)^2$ using substitution method?

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