Maximum incarceration of numbers in an n X n X n number cubes with full incarceration volumes.

Terms

a(0) =0a(1) =0a(2) =21a(3) =292a(4) =1566a(5) =5664a(6) =16375a(7) =40716a(8) =90552a(9) =184576a(10) =350649a(11) =628500a(12) =1072786a(13) =1756512a(14) =2774811a(15) =4249084a(16) =6331500a(17) =9209856a(18) =13112797a(19) =18315396a(20) =25145094a(21) =33988000a(22) =45295551a(23) =59591532a(24) =77479456a(25) =99650304a(26) =126890625a(27) =160090996a(28) =200254842a(29) =248507616