In this paper, we make a substantial step towards an encoding of Cubical Type Theory (CTT) in the Dedukti logical framework. Type-checking CTT expressions features a decision procedure in a de Morgan algebra that so far could not be expressed by the rewrite rules of Dedukti. As an alternative, 2 Layer Type Theories are variants of Martin-Lf Type Theory where all or part of the definitionalequality can be represented in terms of a so-called external equality. We propose to split the encodingby giving an encoding of 2 Layer Type Theories (2LTT) in Dedukti, and a partial encoding of CTTin 2LTT.