I have achieved pointing a subdomain (yoursubdomain.example1.com) from a domain (example1.com) hosted in a environment running WHM (localServer) to an Amazon EC2 instance (cloudServer).
I will explain using Amazon solutions, but Route53 (Amazon Nameserver Service) steps are more or less equivalent in any other environment (create HOSTED ZONE, RECORD SETS, etc). Steps 1 thru 5 are, therefore, Amazon specific and represent background steps beyond the strict scope of this question (yet, IMO, necessary). Steps 6 & 7 answer the question regarding WHM configuration.
Open Amazon EC2 dashboard, and create a new ELASTIC IP;
Select new ELASTIC IP from list (126.96.36.199), click on ACTION, and pick ASSOCIATE ADDRESS from dropdown list;
Select the instance that you want to point your subdomain to and ASSOCIATE;
Open Amazon Route53 >> HOSTED ZONES >> CREATE NEW, insert yoursubdomain.example1.com in the DOMAIN NAME box and CREATE;
Open Amazon Route53, select yoursubdomain.example1.com >> GO TO RECORD SETS >> CREATE RECORD SET, insert your ELASTIC IP (188.8.131.52); choose type A IPV4 ADDRESS and CREATE;
In WHM, open EDIT DNS ZONE and choose your domain from the dropdown list (example1.com).
Go to the bottom of the page and insert at least two of the name servers listed in your Route53 A record (in this case ns-1963.awsdns-53.co.uk. and ns-1963.awsdns-53.co.uk.). DONT FORGET THE "." at the end of the url!!!
You should be all set, use online DNS lookup tools, such as MXTools (choose DNS LOOKUP) or WhatsMyDNs, to verify if everything is set. Propagation is surprinsingly quick, because your master domain did not move, it just points new info (subdomain nameserver) dynamically now.