2X2X2 cube puzzle and a cube stand

A puzzle game comprising:

• a) a cube packing comprising two triangular pyramids, each pyramid having three hexagonal sides rectangular to each other, such that all pyramid vertexes being truncated, and the cube packing being configured for two non-simultaneous functional modes:
• A) a packing mode whereas a cube being positioned between said two triangular pyramids such that each hexagonal side of each triangular pyramid touching a face of said cube;
• and
• B) a stand mode such that:
• (1) a first triangular pyramid laying on a substantially horizontal surface;
• (2) a second triangular pyramid resting on said first triangular pyramid;
• (3) said cube residing in said second triangular pyramid;
• (4) a first vertex of said cube pointing upwards;
• and
• (5) a second vertex of said cube penetrating two pyramid truncated vertexes and pointing downwards;
• b) a large cube packable within said cube packing in said packing mode, said large cube consisting of eight small cubes of a common size;
• c) said eight small cubes consisting of a first group of exactly eight pieces and a second group of exactly 16 pieces, wherein each of said large cube and said small cubes having no substantial apparent vacancy within respective boundaries;
• d) each small cube consisting one piece of said first group and two pieces of said second group;
• and
• e) said first group consisting eight pieces having different shapes and colors as follows:
• A) a piece having a first shape and a first color;
• B) a piece having said first shape and a second color;
• C) a piece having said first shape and a third color;
• D) a piece having a second shape and said first color;
• E) a piece having said second shape and said second color;
• F) a piece having said second shape and said third color;
• G) a piece having a third shape and said first color;
• and H) a piece having said third shape and said second color.