Let A={[\table 2 , 0 , 1 ; 1 , 1 , 0 ; 1 , 0 , 1]}, B= [B_1, B_2, B_3] , where B_1, B_2, B_3 are column matrices, and {\AB}_1={[\table 1 ; 0 ; 0]}, {\AB}_2={[\table 2 ; 3 ; 0 ]}, {\AB}_3={[\table 3 ; 2 ; 1 ]} If α=|B| and β is the sum of all the diagonal elements of B, then α^3+β^3 is equal to [27-Jan-2024 Shift 1]

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