This is not a homework question.
It could accept hydrogen bonds from other molecules, but given that it doesn't have any hydrogens, it would not be able to act as a hydrogen bond donor.
With the oxygens all double bonded to the carbons where would the hydrogen bond to?
Well, what is needed for an atom in a molecule to act as a hydrogen bond acceptor? (hint: read https://en.wikipedia.org/wiki/Hydrogen_bond)
There's nothing preventing a double bonded oxygen from accepting a hydrogen bond.
Hydrogen bonds aren't the same as the bonds between the double bonded C=O. Oxygen and Nitroghen have a very high electronegativity (They love electrons). So in a molecule they are bonded to, they hold most of the negative charge creating poles within the molecule, because if they have the electrons, the other atoms don't leaving them with a positive charge. If another molecule is introduced (say water) that is polar and contains hydrogen, their poles can interact creating an attractive force that's not really a bond but like I said just an attractive force. This interaction is considered hydrogen bonding. So you see it doesn't matter that double bond's exist between the C=O as long as there is dipole attractive forces.
However, in this particular molecule, I don't think the hydrogen bonding would be that strong because it is not all that polar to begin with. But hydrogen bonds could exist because the molecule is slightly polar.
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