Tadashige was the first son of Tadanori SAKAI, a hatamoto (direct retainer of the bakufu, which is a form of Japanese feudal government headed by a shogun) with 5000 koku from the Himeji Domain branch family, but became the main branch's foster child because the lord of Himeji Domain Tadateru SAKAI did not have any biological children.
忠績は姫路藩分家旗本5000石の酒井忠誨の長男であるが、姫路藩藩主酒井忠顕に子がないため、本家の養子となる。