Let's play with 2007!


         
      2007   =  112408635^3 + 9086257^3 - 112428421^3
  
      2007^3 =  1044^3+1119^3+1770^3
          
      2007^4 =  4008^4+ 1997^4+ 6005^4 -6007^4 -4000^4
             =  6005^4+ 1993^4+ 7998^4 -5995^4 -8002^4

      2007^5 =  3087^5- 3123^5+ 2241^5- 1557^5+ 1125^5+ 675^5- 441^5

      2007^6 =  1341^6+ 1899^6+ 2583^6+ 1557^6+ 135^6 -2565^6 -1467^6 -441^6 -1251^6