Yoshitomo Nara’s art is deceptively cute. With wide eyes and seemingly innocent expressions, his figures are portrayed in pastel shades and cartoon-esque scenes across drawings, paintings and sculptures. They draw you in close, only to reveal a dark side: while some kids hold records, others carry knives and guns. All is not what it seems.

Nara’s painted children come with a rock ‘n’ roll attitude reinforced by his passion for music, which is referenced across his paintings and explicitly in an installation at the start of the Hayward show.

Here we find an artist’s shack, with music playing. Peer through the windows and it’s as if Nara has momentarily stepped away – drawings are half finished and models and other ephemera are strewn about. And behind the building is a giant display of classic albums, mostly from the 60s and 70s, chosen by the artist for their influence on his art.

This love for music tracks back to Nara’s early years in Japan’s northern Tōhoku region, where he listened to the Far East Network (FEN): the radio station for American troops stationed in Japan during the Vietnam War. He painted from an early age though his distinctive style – the development of which is revealed in a series of early drawings – came while studying at the Kunstakademie in Düsseldorf. Nara was unable to speak German and used his art to express himself and overcome loneliness, a theme that has remained as strong as music in his work.

His style jumps from immaculately formed paintings and sculptures to rougher works on cardboard and a recent set of stark black and white drawings. A mix of humour, despair and cartoon rage merges with anxiety and the odd political moment. The most poignant of these comes in Under the Hazy Sky from 2012, which Nara painted in the aftermath of the 2011 Fukushima nuclear disaster. The painting depicts a weakened version of one of his archetypal figures, with thin arms and hooded eyes surrounded by a thick fog.

Despite this dark moment, Nara quickly takes us back to his familiar territory of joy delivered with a snarl. The appeal of Nara’s work lies in his ability to bounce from pop culture pleasure – the gift shop at the Hayward will undoubtedly do well during this show – to moments of existentialism and teenage angst. The emotional range here is not especially complex, but Nara’s charm is consistent across 40 years of work.

Yoshitomo Nara is at the Hayward Gallery until August 31; southbankcentre.co.uk