There are certain configurations required between Skpe and CUCM for the connection to work.
It is typically a SIP trunk pointing to one of SKPE's SIP proxy Server.
Outbound calls will be using this trunk and so will the inbound calls.
You need to discuss the level of Service with Skype. This link will give you more information.
http://www.skype.com/intl/en-us/business/sip/get-it-now#paddedContent
Next, you will need to let Skype know that this version of CUCM does not
support SIP Digest authentication, so their side of the trunk will need
to have this disabled.
Lastly, you will need to define a SIP trunk in CUCM with a Route Pattern
pointing to it. More information on SIP trunks on CUCM can be found
here:
Configuring a Trunk,
http://www.cisco.com/en/US/docs/voice_ip_comm/cucm/admin/5_1_3/ccmcfg/b06trunk.html#wp1127633
Trunk Configuration Settings for SIP Trunks
http://www.cisco.com/en/US/docs/voice_ip_comm/cucm/admin/5_1_3/ccmcfg/b06trunk.html#wp1164882