设上往下各层的正方体数目组成数列{an}由题得：a2-a1=2，a3-a2=3…an-an-1=n．把上面各式相加得：an-a1=2+3+4+…+n所以an=a1+2+3+…+n=1+2+3+…+n= n(n+1) 2 ．故 a2005= 2005×(1+2005) 2 =2011015．故选：C．
