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Recently, the author defined multiple Dedekind zeta values \cite{MDZF}associated to a number $K$ field and a cone $C$. In this paper we constructexplicitly non-trivial examples of mixed Tate motives over the ring of integersin $K$, for a real quadratic number field $K$ and a particular cone C. Theperiod of such a motive is a multiple Dedekind zeta values at$(s_1,s_2)=(1,2)$, associated to the pair $(K;C)$, times a nonzero element of$K$.

Periods of Mixed Tate Motives over Real Quadratic Number Rings