The heat conduction problem

What is a solution for the initial boundary-value problem (using separation of variables method)?
$ u_t=4u_x_x,              0<x<1, t>0; $
$ u(x,0)=x^2(1-x),        0\le x\le1; $
$ u(0,t)=0 ;                    u(1,t)=0 ;t\ge0 $

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