Representation of error functional of a cubature formula is set up for an arbitrary function from Sobolev space normalized while using the derivatives of all orders up to the highest one. In comparison with the papers devoted to the issue of setting up the functional representations by the summable functions the Sobolev space here is normalized without pseudodifferential operator. The existence, uniqueness and summability of the representing function are proved. Neither norm nor representation of the functional coincides with those described before at any value of the highest order of the function derivatives in the class considered.