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For this type of computation, it is worth trying with some algorithm different from the default one (Maxima):

sage: integrate(x^3/(exp(x)-1),x,0,infinity, algorithm='giac')
1/15*pi^4

For this type of computation, it is worth trying with some algorithm different from the default one (Maxima):

sage: integrate(x^3/(exp(x)-1),x,0,infinity, algorithm='giac')
1/15*pi^4

EDIT: the above works only for Sage 8.0.beta5 and higher versions (after the ticket https://trac.sagemath.org/ticket/22891 has been merged). This will therefore be available in the next stable release of Sage (8.0).