I believe on the 3x3 there are 1,090,175,792,696,524,800 non-symetric positions which is about 1/40 of the original number. Now the non-symetric positions can be stored in 60 bits per position times the # of positions which equals 65,410,547,561,791,488,000 bits or 8,176,318,445,223,936,000 bytes or ~8,176,318.4 terabytes.

For 4x4 there are 7,401,196,841,564,901,869,874,093,974,498,574,336,000,000,000 positions now assuming that the 1/40 ratio is true (it isn't but hopefully it will be closer than 1/96 (= 1/24*1/2*1/2) ) then the non-symetric positions are 185,029,921,039,122,546,746,852,349,362,464,358,400,000,000. That can be stored in 148 bits per position for a total of 185,029,921,039,122,546,746,852,349,362,464,358,400,000,000 bits or 185,029,921,039,122,546,746,852,349,362,464,358,400,000,000 bytes or ~185,029,921,039,122,546,746,852,349,362,464.4 terabytes or ~1.85*10^32 terabytes.

TL;DR

3x3 = ~8,176,318.4 terabytes

4x4 = ~1.85*10^32 terabytes