960
way 1
smallest cube greater 2000 is 13^3=2197---> surface area = 13*13*6=1014, it stays same if you remove 197 units. (When removing a unit, you remove 3 dimensions but expose the surface of adjacent units so overall number remains unchanged)
way 2
greatest cube smaller 2000 is 12^3=1728 --> surface area = 12*12*6=864
need to add 200-1728=272 unit with minimum addition to surface, it is achieved by 2 layers of 12*12*2=288 units, it adds up 12*2*4=96 (4 sides of 12*12*2 polycube) units, so total area = 864+96=960. Minus 288-272=16 units doesn't change the surface area as explained above.
