A family of special cubic fourfolds with motive of abelian type

Abstract: In this short note, we show that there exist one dimensional families of cubic fourfolds with Chow motive of abelian type and finite dimensional inside every Hassett divisor of special cubic fourfolds. This also implies abelianity and finite dimensionality of the motive of related Hyperk\"ahler varieties, such as the Fano variety of lines and the LLSvS 8fold.