Growing perfect cubes

An (n,a,b)(n,a,b)-perfect double cube is a b×b×bb×b×b sized n  -ary periodic array containing all possible a×a×aa×a×a sized n  -ary array exactly once as subarray. A growing cube is an array whose cj×cj×cjcj×cj×cj sized prefix is an (nj,a,cj)(nj,a,cj)-perfect double cube for j=1,2,…, where cj=njv/3,v=a3 and n1