If you really want to do it yourself, here's a formula:
initial volume = the amount of 6 mg/ml
juice you start with
initial concentration = the nicotine concentration of your starting
juice (6 mg/ml, in this case)
target concentration = the concentration you want in the end (15 mg/ml, in your example)
nicotine concentration = the concentration of the nicotine you're adding (100 mg/ml, in your example)
Amount of nicotine to add
= [initial volume x (target concentration - initial concentration)] / [nicotine concentration - target concentration]
For your example, this would be:
= [initial volume x (15 mg/ml - 6 mg/ml)] / [100 mg/ml - 15 mg/ml]
= [initial volume x 9 mg/ml] / 85 mg/ml