Nature versus nurture is an eternal problem in science, and for most traits it is nearly impossible to determine which plays a larger part. Intelligence is no different, and a definite answer is hard to come by.
A test was conducted by Rick Heber in the late '60s that focused on the children from one specific area in Milwaukee. Forty newborn children were selected, all with mothers with an IQ of below 80. Half of these children were then enrolled in an enrichment program, and the other half were raised as they would be ordinarily. The group in the enrichment program, by the age of 6 had an average IQ of 120.7, and the control group had an IQ of 87.2. This study seems to show that nurture plays a big part in intelligence.
Researchers at the UCLA have found that intelligence is directly related to the quality of the brain's "axons," which are basically the wires that send information through the brain. The discovery that these axons have an effect of intelligence adds to the argument for intelligence being an inheritable trait, because genes are thought to have an effect on these axons.