Let L be a lattice. If K is a sublattice of L , then L is called an extension of K . Lattice extension concept was elaborately studied by G. Grätzer and E. T. Schmidt in their papers [6], [7], [9], [10]. A lattice L is said to be simple if it has no non-trivial congruences. A finite graded poset P is said to be Eulerian if its Möbius function assumes the value μ( x, y ) = (-1) l(x, y) for all x £ y in P , where l ( x, y ) = ρ( y ) - ρ( x ) and ρ is the rank function on P . In this paper, we exhibit various possible Eulerian extensions which are simple for any given Eulerian lattice L and we prove that there exists a congruence-preserving extension of an Eulerian lattice. The cubic extension of a lattice was defined by G. Grätzer and E. T. Schmidt in [11]. We show that the cubic extension becomes a congruence-preserving extension when the lattice is Eulerian.