It's not possible to easily find out the cost for backbone traffic, because it's done almost exclusively via barter, which in particular case of IP traffic is called peering. Also, typically peering isn't even formalized in any document.
Excerpt from the Survey of Characteristics of Internet Carrier Interconnection Agreements
Of the total analyzed agreements, 698 (0.49%) were formalized in
written contracts. The remaining 141,512 (99.51%) were “handshake”
agreements in which the parties agreed to informal or commonly
understood terms without creating a written document. The common
understanding is that only routes to customer networks are exchanged,
that BGP version 4 is used to communicate those routes, and that each
network will exercise a reasonable duty of care in cooperating to
prevent abusive or criminal misuse of the network. This huge number
of informal agreements are arrived at by the “peering coordinators”
or carrier-interconnection negotiation staff of the networks, often at
self-organized regional or global “peering forums” that take place
many times each year.
Of the agreements we analyzed, 141,836 (99.73%) had symmetric terms,
in which each party gave and received the same conditions as the
other; only 374 (0.27%) had asymmetric terms, in which the parties
gave and received conditions with speciﬁcally deﬁned differences.
Typical examples of asymmetric agreements are ones in which one of the
parties compensates the other for routes that it would not otherwise
receive (known as “paid peering”), or in which one party is
required to meet terms or requirements imposed by the other (“minimum
peering requirements”). In the more common symmetric relationship,
the parties to the agreement simply exchange customer routes with each
other, without settlements or other requirements.
Besides that, "how much does it costs to sent X GBs of data?" isn't good question, as total amount of traffic sent is just one measure, hardly ever used by higher tier operators. Peak traffic or allocated capacity are more common.
Ok, so being that being said, what it costs Deutsche Telekom to send it's clients traffic would be the cost of operating it's backbone and lower tier networks connecting to the customers. Problem is, that it's again hard to calculate what the cost would be if you get more traffic, more clients etc.
Calculating these cost has been studied for example in paper "Sharing the Cost of Backbone Networks"
What contributes to the cost of a backbone? The cost of a network consists of CAPEX and OPEX for all devices and Points-of-Presence
(PoPs). The CAPEX is the one-time cost paid whenever equipment is
bought and installed. It depends on the amount of traﬃc the device
must carry at a speciﬁc level of Quality-ofService (QoS). A key
observation is that the capacity needed to guarantee a certain QoS
depends on the peak traﬃc that needs to be carried. This is because
for a given capacity, QoS is minimized when the traﬃc peaks. The OPEX
corresponds to operational costs such as real estate, energy, and
personnel. It also depends on the amount of traﬃc and the QoS;
however, that dependence is more elastic. The cost sharing policies we
discuss are generic enough to capture both CAPEX and OPEX with
Why is it diﬃcult to split cost among
customers? From the above discussion, one may conclude that splitting
the cost among customers is straightforward: for each device of the
network each customer should pay in proportion to his contribution to
the peak traﬃc carried by the device and then sum up over all devices.
Things, however, are not that simple:
Accounting complications. It
is diﬃcult to know for each network device the contribution of each
customer to its peak. This is because backbone operators need to
measure and keep state at many points in the network, which requires
costly monitoring equipments. In addition, computing traﬃc rates
introduces the problem of identifying the appropriate time-scale for
the computation owing to the limited resources of the monitoring
Liability complications. If we were to build from scratch a
new network for a ﬁxed set of customers of known demand, then the cost
attributed to each customer should be proportional to the sum of its
contributions to the peaks of individual devices. Splitting costs
based on the contribution to the peak is indeed exact, but only for
this “oﬄine problem”. In reality, however, networks are not built in
one-shot but are rather organically grown with the addition of new
customers and the ramping up of their traﬃc. Under this more realistic
case, peak-based cost-sharing is not guaranteed to be fair. Consider
for example the case in which a network is already operating at the
maximum utilization allowed by QoS constraints and a small new
customer triggers an expensive upgrade that leads to a new network
with plentiful unallocated capacity (upgrades typically involve large
jumps, e.g., 1Gbps to 2.5Gbps, to 10Gbps, etc.). Peak-based cost
sharing would attribute to the new customer only a small fraction of
the overall cost. Is that fair? The answer depends on what happens
with the unallocated capacity. If the network can easily sell it to
new or existing customers then indeed it is fair. If, however, selling
this leftover capacity is not guaranteed, then the new customer should
have a larger liability for the upgrade costs.
I don't have access to detailed Deutsche Telekom financial report, but from the global one you can see that in 2012 their operating expenses were 18.3 billion euros, and they've closed they year with net loss of 5.3 billion euros.